evidences for clustering

Cluster Models

P. Descouvemont

Physique Nuclaire Thorique et Physique Mathmatique, CP229,Universit Libre de Bruxelles, B1050 Bruxelles - BelgiumEvidences for clusteringCluster models: non-microscopic (nucleus-nucleus interaction) microscopic (NN interaction) continuum statesApplication 1 : 5H and 5He (microscopic 3 body)Application 2 : triple a process (non-microscopic)Application 3: 18F(p,a)15O (reaction, microscopic 2 body)Conclusions

IntroductionClustering: well known effect in light nuclei

Nucleons are grouped in clustersBest candidate: a particle (high binding energy, almost elementary particle) Ikeda diagram: cluster states near a threshold (8Be, 20Ne, etc

Halo nuclei: special case of cluster states

Beyond the nucleon level: hypernuclei quarks etc.

1. Evidence for clusteringLarge distance between the clusters wave function important at large distances Example :a+16O

Comparison of radii:a~1.4 fm, 16O~2.7 fmFor 20Ne 0+: 1/2=3.9 fmFor 20Ne 1-: 1/2=5.6 fm 20Nea+16O0+4+1-2+3-clusterNon-cluster

Graph1

0.17680.02159

0.31490.07979

0.38440.1589

0.37060.2367

0.27710.2905

0.12470.3027

-0.053980.2652

-0.22160.1812

-0.34440.06443

-0.399-0.06415

-0.3762-0.181

-0.2824-0.2649

-0.1367-0.3014

0.03355-0.285

0.1982-0.2197

0.3301-0.1178

0.40940.003186

0.42620.1238

0.38050.226

0.28150.2959

0.1450.3251

-0.010010.3117

-0.1640.2595

-0.29960.1765

-0.40370.07358

-0.4676-0.03719

-0.4881-0.1444

-0.4663-0.2382

-0.4069-0.3112

-0.317-0.3589

-0.2051-0.3793

-0.08017-0.3729

0.04955-0.342

0.1768-0.2904

0.2956-0.2225

0.4016-0.1432

0.4921-0.0571

0.56560.03148

0.62170.1189

0.6610.2022

0.68480.2791

0.69480.3481

0.69280.4082

0.68080.4591

0.66090.5007

0.63480.5335

0.60420.5579

0.57050.5747

0.53510.5848

0.49880.5889

0.46260.588

0.42710.5829

0.39270.5742

0.35990.5627

0.32880.549

0.29960.5336

0.27240.5171

0.24710.4997

0.22390.4818

0.20250.4637

0.18290.4456

0.16510.4278

0.14890.4102

0.13420.3931

0.12080.3765

0.10880.3605

0.097860.3451

0.088030.3303

0.079170.3162

0.07120.3027

0.064020.2898

0.057560.2776

0.051750.266

0.046530.255

0.041840.2445

0.037630.2346

0.033850.2252

0.030440.2163

0.027390.2079

0.024640.1999

0.022180.1923

0.019960.1852

0.017970.1784

0.016180.172

0.014570.1659

0.013120.1601

0.011820.1546

0.010650.1494

0.0096020.1445

0.0086550.1398

0.0078030.1354

0.0070360.1312

0.0063460.1272

0.0057240.1234

0.0051640.1197

0.004660.1163

0.0042060.113

0.0037960.1099

0.0034270.1069

0.0030950.1041

0.00279510.1

0.00252410.2

0.0022810.3

0.0020610.4

0.00186210.5

0.00168310.6

0.00152110.7

0.00137510.8

0.00124310.9

0.00112411

0.00101711.1

0.000919611.2

0.000831911.3

0.000752711.4

0.000681111.5

0.000616411.6

0+

1-

r (fm)

wave function

a+16O wave function

Feuil1

0.12.24E-01-2.53E-012.57E-01-2.47E-012.23E-01-1.74E-01

0.24.37E-01-4.77E-014.70E-01-4.40E-013.89E-01-2.99E-01

0.36.27E-01-6.46E-016.03E-01-5.37E-014.57E-01-3.40E-01

0.47.86E-01-7.42E-016.35E-01-5.19E-014.09E-01-2.87E-01

0.59.08E-01-7.56E-015.61E-01-3.91E-012.59E-01-1.55E-01

0.69.90E-01-6.88E-013.95E-01-1.80E-014.45E-021.99E-02

0.71.03E+00-5.48E-011.66E-016.81E-02-1.81E-011.89E-01

0.81.04E+00-3.53E-01-8.94E-023.03E-01-3.63E-013.08E-01

0.91.01E+00-1.24E-01-3.31E-014.77E-01-4.59E-013.47E-01

19.49E-011.16E-01-5.25E-015.60E-01-4.50E-012.97E-01

1.18.73E-013.47E-01-6.45E-015.38E-01-3.40E-011.72E-01

1.27.83E-015.51E-01-6.78E-014.18E-01-1.56E-015.48E-03

1.36.88E-017.15E-01-6.25E-012.25E-016.25E-02-1.63E-01

1.45.91E-018.33E-01-4.95E-01-6.13E-032.68E-01-2.94E-01

1.54.98E-019.02E-01-3.10E-01-2.37E-014.20E-01-3.59E-01

1.64.11E-019.26E-01-9.08E-02-4.31E-014.93E-01-3.46E-01

1.73.34E-019.11E-011.37E-01-5.63E-014.75E-01-2.61E-01

1.82.67E-018.65E-013.53E-01-6.17E-013.74E-01-1.23E-01

1.92.09E-017.96E-015.41E-01-5.92E-012.10E-013.88E-02

21.62E-017.12E-016.88E-01-4.94E-011.23E-021.94E-01

2.11.23E-016.22E-017.91E-01-3.41E-01-1.87E-013.15E-01

2.29.27E-025.32E-018.48E-01-1.52E-01-3.61E-013.83E-01

2.36.87E-024.45E-018.64E-015.26E-02-4.86E-013.89E-01

2.45.03E-023.66E-018.46E-012.53E-01-5.50E-013.37E-01

2.53.64E-022.96E-018.00E-014.33E-01-5.49E-012.36E-01

2.62.60E-022.35E-017.36E-015.82E-01-4.89E-011.02E-01

2.71.84E-021.84E-016.60E-016.95E-01-3.78E-01-4.40E-02

2.81.28E-021.43E-015.79E-017.69E-01-2.33E-01-1.85E-01

2.98.90E-031.09E-014.98E-018.07E-01-6.66E-02-3.06E-01

36.11E-038.20E-024.21E-018.12E-011.05E-01-3.95E-01

3.14.15E-036.11E-023.50E-017.91E-012.69E-01-4.45E-01

3.22.80E-034.51E-022.87E-017.49E-014.16E-01-4.55E-01

3.31.88E-033.30E-022.32E-016.93E-015.39E-01-4.27E-01

3.41.25E-032.39E-021.85E-016.27E-016.35E-01-3.65E-01

3.58.23E-041.71E-021.46E-015.58E-017.03E-01-2.77E-01

3.65.39E-041.22E-021.14E-014.89E-017.43E-01-1.72E-01

3.73.52E-048.63E-038.86E-024.22E-017.59E-01-5.52E-02

3.82.28E-046.06E-036.80E-023.60E-017.54E-016.41E-02

3.91.47E-044.23E-035.18E-023.03E-017.31E-011.80E-01

49.42E-052.94E-033.92E-022.53E-016.96E-012.89E-01

4.16.01E-052.03E-032.94E-022.09E-016.51E-013.86E-01

4.23.82E-051.39E-032.19E-021.71E-016.01E-014.69E-01

4.32.42E-059.51E-041.63E-021.39E-015.47E-015.37E-01

4.41.53E-056.47E-041.20E-021.12E-014.93E-015.90E-01

4.59.61E-064.39E-048.82E-039.02E-024.40E-016.29E-01

4.66.03E-062.96E-046.45E-037.20E-023.89E-016.55E-01

4.73.77E-062.00E-044.70E-035.72E-023.42E-016.68E-01

4.82.35E-061.34E-043.41E-034.52E-022.98E-016.71E-01

4.91.46E-068.97E-052.47E-033.56E-022.58E-016.64E-01

59.09E-076.00E-051.78E-032.79E-022.23E-016.51E-01

5.15.63E-074.00E-051.28E-032.18E-021.91E-016.32E-01

5.23.49E-072.66E-059.21E-041.70E-021.63E-016.08E-01

5.32.15E-071.77E-056.60E-041.32E-021.39E-015.81E-01

5.41.33E-071.17E-054.72E-041.02E-021.18E-015.52E-01

5.58.19E-087.75E-063.37E-047.92E-039.99E-025.22E-01

5.65.04E-085.13E-062.40E-046.12E-038.43E-024.91E-01

5.73.10E-083.39E-061.71E-044.72E-037.10E-024.60E-01

5.81.90E-082.23E-061.22E-043.63E-035.96E-024.30E-01

5.91.17E-081.47E-068.64E-052.79E-035.00E-024.00E-01

67.17E-099.70E-076.13E-052.14E-034.19E-023.72E-01

6.14.40E-096.39E-074.35E-051.65E-033.51E-023.44E-01

6.22.70E-094.20E-073.08E-051.26E-032.93E-023.19E-01

6.31.65E-092.76E-072.18E-059.66E-042.44E-022.94E-01

6.41.01E-091.82E-071.54E-057.40E-042.04E-022.72E-01

6.56.19E-101.19E-071.09E-055.66E-041.70E-022.50E-01

6.63.79E-107.84E-087.73E-064.33E-041.42E-022.30E-01

6.72.32E-105.15E-085.46E-063.31E-041.18E-022.12E-01

6.81.42E-103.38E-083.86E-062.53E-049.81E-031.95E-01

6.98.67E-112.22E-082.73E-061.93E-048.16E-031.79E-01

75.30E-111.46E-081.93E-061.48E-046.78E-031.65E-01

7.13.24E-119.55E-091.36E-061.13E-045.64E-031.51E-01

7.21.98E-116.27E-099.62E-078.61E-054.69E-031.39E-01

7.31.21E-114.11E-096.79E-076.57E-053.90E-031.27E-01

7.47.41E-122.70E-094.80E-075.02E-053.24E-031.17E-01

7.54.53E-121.77E-093.39E-073.83E-052.69E-031.07E-01

7.62.77E-121.16E-092.39E-072.93E-052.24E-039.86E-02

7.71.69E-127.62E-101.69E-072.23E-051.86E-039.05E-02

7.81.04E-125.00E-101.19E-071.71E-051.55E-038.31E-02

7.96.33E-133.28E-108.43E-081.30E-051.28E-037.63E-02

83.87E-132.15E-105.95E-089.94E-061.07E-037.01E-02

8.12.36E-131.41E-104.20E-087.59E-068.87E-046.44E-02

8.21.45E-139.26E-112.97E-085.79E-067.38E-045.92E-02

8.38.84E-146.07E-112.10E-084.42E-066.13E-045.44E-02

8.45.40E-143.98E-111.48E-083.38E-065.10E-045.00E-02

8.53.30E-142.61E-111.05E-082.58E-064.24E-044.59E-02

8.62.02E-141.72E-117.39E-091.97E-063.52E-044.22E-02

8.71.23E-141.13E-115.22E-091.50E-062.93E-043.88E-02

8.87.55E-157.38E-123.69E-091.15E-062.44E-043.57E-02

8.94.62E-154.85E-122.60E-098.78E-072.03E-043.29E-02

92.82E-153.18E-121.84E-096.70E-071.69E-043.02E-02

9.11.73E-152.09E-121.30E-095.12E-071.40E-042.78E-02

9.21.06E-151.37E-129.19E-103.91E-071.17E-042.56E-02

9.36.45E-168.99E-136.49E-102.99E-079.71E-052.36E-02

9.43.95E-165.90E-134.59E-102.28E-078.08E-052.17E-02

9.52.41E-163.87E-133.24E-101.75E-076.73E-052.00E-02

9.61.48E-162.54E-132.29E-101.33E-075.60E-051.85E-02

9.79.03E-171.67E-131.62E-101.02E-074.66E-051.70E-02

9.85.52E-171.10E-131.14E-107.79E-083.88E-051.57E-02

9.93.38E-177.19E-148.09E-115.96E-083.23E-051.45E-02

102.07E-174.72E-145.72E-114.55E-082.69E-051.33E-02

10.11.26E-173.10E-144.04E-113.48E-082.24E-051.23E-02

10.27.73E-182.04E-142.86E-112.66E-081.87E-051.13E-02

10.34.73E-181.34E-142.02E-112.03E-081.55E-051.05E-02

10.42.89E-188.77E-151.43E-111.56E-081.29E-059.66E-03

10.51.77E-185.76E-151.01E-111.19E-081.08E-058.91E-03

10.61.08E-183.78E-157.14E-129.09E-098.98E-068.23E-03

10.76.63E-192.48E-155.05E-126.95E-097.48E-067.60E-03

Feuil1

0.2242-0.2530.257-0.24660.223

0.4366-0.47680.4701-0.43960.3892

0.6268-0.64590.6032-0.53720.4566

0.7859-0.74190.6346-0.51930.4088

0.9079-0.75560.5605-0.39080.2587

0.9897-0.68770.3947-0.180.04454

1.031-0.54790.16560.06808-0.1806

1.035-0.3529-0.089440.3026-0.3626

1.005-0.124-0.33120.4773-0.4594

0.94890.1164-0.52470.56-0.4504

0.87260.3471-0.64470.5378-0.3402

0.78330.5508-0.6780.4181-0.1555

0.68750.7148-0.62460.2250.06252

0.59080.8325-0.4954-0.006130.2679

0.49770.902-0.3097-0.23660.4204

0.41140.9262-0.09083-0.4310.4928

0.33410.91110.1373-0.56280.4749

0.26670.86470.3533-0.61730.3737

0.20940.79560.5406-0.59180.2098

0.16190.71230.688-0.49440.01226

0.12340.62240.7906-0.341-0.1874

0.092690.53190.8481-0.1516-0.3606

0.06870.44540.86440.0526-0.4857

0.050280.36610.84590.2525-0.5498

0.036350.29590.80040.4325-0.5493

0.025980.23530.7360.5819-0.4887

0.018360.18440.660.6947-0.3784

0.012840.14250.57910.7691-0.2326

0.0088980.10870.49810.8068-0.06659

0.0061060.081980.4210.81220.1048

0.0041540.061130.35010.79080.269

0.0028030.04510.28690.74880.4161

0.0018760.032960.2320.69250.5394

0.0012470.023870.18530.62740.6353

0.00082270.017140.14640.55820.7028

0.00053940.012210.11440.48880.7431

0.00035150.0086310.088610.4220.7589

0.00022780.0060620.068020.35970.7536

0.00014680.0042310.051790.30310.7313

0.000094170.0029350.039150.25280.6959

0.000060130.0020260.029390.20890.6513

0.000038230.0013910.021930.17120.6009

0.000024210.00095060.016270.13920.5474

0.000015280.0006470.012010.11240.4932

0.000009610.00043870.0088220.090210.4401

0.0000060260.00029640.0064530.071990.3894

0.0000037680.00019960.0047020.057160.3419

0.0000023510.0001340.0034130.045180.2981

0.0000014630.000089740.002470.035560.2584

0.00000090850.000059950.0017820.027890.2228

0.00000056320.000039960.0012830.02180.1912

0.00000034850.000026580.00092110.016990.1634

0.00000021530.000017650.00065990.01320.1391

0.00000013290.000011710.00047190.010240.118

0.00000008190.000007750.00033690.0079210.09986

0.00000005040.0000051250.00024020.0061170.08427

0.0000000310.0000033850.0001710.0047170.07096

0.0000000190.0000022340.00012160.0036310.05963

0.00000001170.0000014730.000086360.0027920.05002

0.00000000720.00000097010.000061290.0021440.0419

0.00000000440.00000063870.000043460.0016450.03505

0.00000000270.00000042020.00003080.0012610.02928

0.00000000170.00000027630.000021810.00096620.02444

0.0000000010.00000018160.000015440.00073970.02039

0.00000000060.00000011930.000010920.0005660.01699

0.00000000040.00000007840.0000077250.00043290.01415

0.00000000020.00000005150.0000054620.00033090.01178

0.00000000010.00000003380.000003860.00025290.009805

0.00000000010.00000002220.0000027280.00019320.008156

0.00000000010.00000001460.0000019270.00014760.006783

00.00000000960.0000013620.00011270.00564

00.00000000630.00000096180.000086090.004689

00.00000000410.00000067930.000065740.003897

00.00000000270.00000047980.000050190.003239

00.00000000180.00000033880.000038320.002692

00.00000000120.00000023930.000029250.002237

00.00000000080.0000001690.000022330.001859

00.00000000050.00000011930.000017050.001545

00.00000000030.00000008430.000013020.001284

00.00000000020.00000005950.0000099370.001067

00.00000000010.0000000420.0000075870.0008872

00.00000000010.00000002970.0000057930.0007375

00.00000000010.0000000210.0000044230.0006131

000.00000001480.0000033780.0005097

000.00000001050.0000025790.0004238

000.00000000740.000001970.0003524

000.00000000520.0000015040.000293

000.00000000370.0000011490.0002437

000.00000000260.00000087760.0002027

000.00000000180.00000067040.0001686

000.00000000130.00000051220.0001403

000.00000000090.00000039130.0001167

000.00000000060.0000002990.00009713

000.00000000050.00000022840.00008083

000.00000000030.00000017460.00006727

000.00000000020.00000013340.00005599

000.00000000020.0000001020.00004661

000.00000000010.00000007790.0000388

000.00000000010.00000005960.0000323

000.00000000010.00000004550.0000269

0000.00000003480.0000224

0000.00000002660.00001865

0000.00000002030.00001554

0000.00000001560.00001294

0000.00000001190.00001078

0000.00000000910.00000898

0000.0000000070.000007482

Feuil2

0.11.77E-010.12.16E-02

0.23.15E-010.27.98E-02

0.33.84E-010.31.59E-01

0.43.71E-010.42.37E-01

0.52.77E-010.52.91E-01

0.61.25E-010.63.03E-01

0.7-5.40E-020.72.65E-01

0.8-2.22E-010.81.81E-01

0.9-3.44E-010.96.44E-02

1-3.99E-011-6.42E-02

1.1-3.76E-011.1-1.81E-01

1.2-2.82E-011.2-2.65E-01

1.3-1.37E-011.3-3.01E-01

1.43.36E-021.4-2.85E-01

1.51.98E-011.5-2.20E-01

1.63.30E-011.6-1.18E-01

1.74.09E-011.73.19E-03

1.84.26E-011.81.24E-01

1.93.81E-011.92.26E-01

22.82E-0122.96E-01

2.11.45E-012.13.25E-01

2.2-1.00E-022.23.12E-01

2.3-1.64E-012.32.60E-01

2.4-3.00E-012.41.77E-01

2.5-4.04E-012.57.36E-02

2.6-4.68E-012.6-3.72E-02

2.7-4.88E-012.7-1.44E-01

2.8-4.66E-012.8-2.38E-01

2.9-4.07E-012.9-3.11E-01

3-3.17E-013-3.59E-01

3.1-2.05E-013.1-3.79E-01

3.2-8.02E-023.2-3.73E-01

3.34.96E-023.3-3.42E-01

3.41.77E-013.4-2.90E-01

3.52.96E-013.5-2.23E-01

3.64.02E-013.6-1.43E-01

3.74.92E-013.7-5.71E-02

3.85.66E-013.83.15E-02

3.96.22E-013.91.19E-01

46.61E-0142.02E-01

4.16.85E-014.12.79E-01

4.26.95E-014.23.48E-01

4.36.93E-014.34.08E-01

4.46.81E-014.44.59E-01

4.56.61E-014.55.01E-01

4.66.35E-014.65.34E-01

4.76.04E-014.75.58E-01

4.85.71E-014.85.75E-01

4.95.35E-014.95.85E-01

54.99E-0155.89E-01

5.14.63E-015.15.88E-01

5.24.27E-015.25.83E-01

5.33.93E-015.35.74E-01

5.43.60E-015.45.63E-01

5.53.29E-015.55.49E-01

5.63.00E-015.65.34E-01

5.72.72E-015.75.17E-01

5.82.47E-015.85.00E-01

5.92.24E-015.94.82E-01

62.03E-0164.64E-01

6.11.83E-016.14.46E-01

6.21.65E-016.24.28E-01

6.31.49E-016.34.10E-01

6.41.34E-016.43.93E-01

6.51.21E-016.53.77E-01

6.61.09E-016.63.61E-01

6.79.79E-026.73.45E-01

6.88.80E-026.83.30E-01

6.97.92E-026.93.16E-01

77.12E-0273.03E-01

7.16.40E-027.12.90E-01

7.25.76E-027.22.78E-01

7.35.18E-027.32.66E-01

7.44.65E-027.42.55E-01

7.54.18E-027.52.45E-01

7.63.76E-027.62.35E-01

7.73.39E-027.72.25E-01

7.83.04E-027.82.16E-01

7.92.74E-027.92.08E-01

82.46E-0282.00E-01

8.12.22E-028.11.92E-01

8.22.00E-028.21.85E-01

8.31.80E-028.31.78E-01

8.41.62E-028.41.72E-01

8.51.46E-028.51.66E-01

8.61.31E-028.61.60E-01

8.71.18E-028.71.55E-01

8.81.07E-028.81.49E-01

8.99.60E-038.91.45E-01

98.66E-0391.40E-01

9.17.80E-039.11.35E-01

9.27.04E-039.21.31E-01

9.36.35E-039.31.27E-01

9.45.72E-039.41.23E-01

9.55.16E-039.51.20E-01

9.64.66E-039.61.16E-01

9.74.21E-039.71.13E-01

9.83.80E-039.81.10E-01

9.93.43E-039.91.07E-01

103.10E-03101.04E-01

10.12.80E-03

10.22.52E-03

10.32.28E-03

10.42.06E-03

10.51.86E-03

10.61.68E-03

10.71.52E-03

10.81.38E-03

10.91.24E-03

111.12E-03

11.11.02E-03

11.29.20E-04

11.38.32E-04

11.47.53E-04

11.56.81E-04

11.66.16E-04

Feuil2

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

0+

1-

r (fm)

wave function

a+16O wave function

Feuil3

Feuil4

Feuil5

Evidence for clusteringLarge reduced width

Defines the reduced width g2 (Pl=penetration factor)gW2=Wigner limit=32/2ma27Li: a cluster states and neutron cluster statesq2(a)=0.52 q2(n)=0q2(a)=0.01 q2(n)=0.26

Evidence for clusteringExotic cluster structure: 6He+6He in 12Be M. Freer et al, Phys. Rev. Lett. 82 (1999) 1383 Particular cluster structure: halo nuclei: 11Be=10Be+n 6He=a+n+n neutron=simplest clusterRotational band: E(J)=E0+2J(J+1)/2mR2With R=distance estimateCalculation: P.D., D. Baye, Phys. Lett. B505 (2001) 71 Mixing of 6He+6He and a+8He

Cluster models vs ab initio modelscluster models: assume a cluster structure effective nucleon-nucleon interaction direct access to continuum states microscopic (full antisymmetrization, depend on all nucleons) non microscopic (nucleus-nucleus interaction) semi-microscopic (approximate treatment of antisymmetrization) ab initio models: more general try to determine a cluster structure realistic nucleon-nucleon interaction Antisymmetrized Molecular Dynamics (AMD) Fermionic Molecular Dynamics (FMD) No Core Shell Model (NCSM) Greens Function Monte Carlo Etc

2. Cluster ModelsSeveral variants Non microscopic 2 clusters nucleus-nucleus interaction 3 clusters

Microscopic: 2 clusters nucleon-nucleon interaction 3 clustersyx

Cluster Models2-cluster models General description Microscopic approach: The generator coordinate method (GCM) Continuum states: the R-matrix method

3-cluster models Hyperspherical coordinates General description

2-body modelsMicroscopic (+cluster approx.) RGM, GCM rNon-microscopic: 2 particles without structure = potential modelrex: a+a, p+16O, etc.F1 ,F2=internal wave functionsSolved by the GCMex: 12C+a, 18F+p, etc.

The wave functions are expanded on a gaussian basis 1. potential model (non microscopic) Schrdinger equation:Expansion:

r=quantal relative coordinate Rn=generator coordinate (variational calculation)

The Generator Coordinate Method (GCM) for 2 clusters

2. MicroscopicSlater Determinants matrix elements between Slater determinants (projection numerical) can be extended to 3-clustersThe Generator Coordinate Method (GCM) for 2 clusters the basis functions are projected Slater determinants (b1=b2=b) variational calculation needs matrix elementsGCM expansionRGM notationGCM notation

Continuum states Necessary for reactions Exotic nuclei: low Q value continuum important Simple for 2 clusters, difficult for 3 clusters Various methods: Exact: calculation of the phase shift Approximations: Complex scaling, Analytic continuation (ACCC), box, etc. (in general, only resonances) Use of the R-matrix method: the space is divided into 2 regions (radius a)Internal: r a: Nuclear + coulomb interactions : antisymetrization importantExternal: r > a: Coulomb only : antisymetrization negligible

The R-matrix method: phase-shift calculation2 body calculations (spins zero)Internal wave function: combination of Slater determinantsExternal wave function: Coulomb (Ul=collision matrix)Bloch-Schrdinger equation:With L = Bloch operator restore the hermiticity of H over the internal region) ensures

The R-matrix method: phase-shift calculationSolution of the Bloch-Schrdinger equation:R-matrix equations N+1 unknown quatities (Ul, fl(Rn)), N+1 equations I=matrix element over the internal region stability with the channel radius a is a strong test

3-body models: Hyperspherical coordinates y1x1Jacobi coordinates x1, y13 sets (xi, yi), i=1,2,3Hyperspherical coordinates:6 coordinatesHamiltonian:

Kinetic energyWith K2(W) = angular operator (equivalent to L2 in two-body systems)

Eigenfunctions:=hyperspherical harmonics Eigenvalues : K(K+4) With lx, ly = angular momenta associated with x, yK = hypermomentFK(a) = Jacobi polynomial

Spin: with S = total spin

Schrdinger equationYJMp is expanded over the hyperspherical harmonicsTo be determinedKnown functions hyperspherical harmonics

g=lx,ly,L,S Set of equations for Truncation at K = Kmax Can be extended to 4-body, 5-body, etc

Three-body Models Hamiltonian

y1x1Non microscopicMicroscopicHamiltonian:

Vij=nucleus-nucleus interaction Problems with forbidden statesEx: 6He=a+n+n 12C=a+a+a 14Be=12Be+n+nVij=nucleon-nucleon interactionEx: 6He=a+n+n 5H=t+n+nProjection: 7-dim integrals

3. Application to 5H and 5HeA. Adahchour and P.D., Nucl. Phys. A 813 (2008) 2523.1Introduction 5H unbound, with N/Z=4: very large value Expected 3-body structure: 3H+n+n Many works:experiment theory Difficult for theory and experiment (unbound AND 3-body structure) still large uncertainties on ground state (Energy, width) level scheme? Isospin symmetry expected 5He(T=3/2) analog states (suggested by Ter-Akopian et al., EPJ A25 (2005) 315)

Application to 5H and 5He3.2 Conditions of the calculation: microscopic 3-cluster NN interaction: Minnesota H=H0+u*V (u=admixture parameter in the Minnesota interaction: u~1)From 3He+p: u=1.12

Application to 5H and 5He5H=3H+n+nTz=3/2,T=3/2n5He=3He+n+n coupled with 3H+n+pTz=1/2, T=1/2,3/2Cluster structure:Main difficulty: unbound states need for specific methods: ACCCxy

Application to 5H and 5He3.3 Analytic Continuation in the Coupling Constant (ACCC) [V.I. Kukulin et al., J. Phys. A 10 (1977) 33]Write H as H=H0+lV (l=1 is the physical value, E(l=1)>0 unbound state)Determine l0 such as E(l0)=0For l > l0 : E(l) l0 : x real, k imaginary, E real l0 determine ci,dj Use l=1 k complex Main problem: stability!Pad approximant

Application to 5H and 5He(T=3/2)3H+n+p3He+n+nT=3/2 state?? 3-body decay: a+n and t+d forb.5H,5He5H5HeT=1/2 states: a+n structure3H+n+n4He+n

Application to 5H and 5He(T=3/2)5Hci(r) expanded in gaussians centred at R = Generator Coordinate MethodEnergy curves E(R): eigenvalue for a fixed R valueConvergence with KmaxDifferent J valuesMicroscopic wave function: 1/2+ expected to be g.s. fast convergence

Graph1

11.064613.523711.026827.878

6.419558.64367.335220.0437

2.408394.527054.064411.3488

1.163833.045272.910635.69138

1.463272.900872.854953.07553

1.524932.691392.672822.07677

1.313362.358082.350241.66594

1.107112.044982.041491.43146

1/2-

5/2+

3/2+

1/2+

J=1/2+

J=3/2+

J=5/2+

J=1/2-

R (fm)

E(R) (MeV)

5H

CE2

J=1/2+,T=3/2

1.511.7220.924.739.7943.7544.1446.3249.2249.8754.0855.3758.166.0266.768.5670.3370.9771.3573.3576.6977.0980.17

37.0113.9115.9530.8533.2734.1735.6437.7439.3141.7143.5545.0454.1155.756.9658.7559.259.9662.6163.163.5474.5975.8576.7378.0579.1981.7182.7884.9585.195.4295.796.5898.74102.43104.66106.01107.52115.7116.15116.54119.31122.9127.94128.96137.26

4.52.938.388.8820.7921.3623.424.0824.7927.5928.0530.9231.3239.6541.7742.844.2444.645.1346.5447.2747.3957.8260.3360.9261.4362.7564.2465.0366.4466.5178.5278.6478.8280.8183.384.6785.8886.7796.9497.4898.03100.09102.7105.41106.29110.62

61.635.565.7111.6813.8314.8515.4716.7917.8417.921.0521.2127.2628.1930.2831.2931.8632.2932.7933.3833.441.8144.8845.1945.8246.7947.3548.0748.8448.8960.4860.8260.9962.3963.5864.565.4365.7976.4177.7178.1379.4780.7982.3582.9884.88

7.51.894.364.526.529.379.8410.1311.5311.8212.8514.4114.518.4818.7421.421.8322.9123.0223.2723.5123.5529.5132.6432.7733.6334.2434.3534.935.2535.2745.3145.6745.7546.8547.0847.8948.4948.5758.3259.9360.2461.1261.4362.562.963.69

91.923.723.814.26.816.987.247.958.5510.2410.2510.2912.5613.2315.715.7616.7616.917.0317.0817.221.1523.9624.1225.1525.4425.525.7125.8325.8634.1234.2634.335.0835.2235.7336.0936.144.2645.8746.1146.4346.7147.3147.5447.88

10.51.693.143.23.255.15.35.775.976.647.677.698.29.019.7711.7712.1112.7512.8412.8712.8913.0215.6717.9718.3919.3519.3919.4819.519.5419.5926.0926.1426.2526.9627.0127.2427.4427.4633.9935.5235.5935.7236.1236.3536.4736.63

121.472.592.752.783.944.334.794.835.396.016.026.66.847.579.189.599.9510.0610.0710.1810.2612.0413.9314.4815.1715.1915.1915.315.3315.4320.3720.4520.6121.1421.3321.4521.4621.5426.6627.8928.0628.2528.4828.5628.6128.71

T=1/2

1.5-11.795.179.3815.7517.9327.4832.0636.0236.0236.6538.8640.3640.8141.4742.343.3745.347.3549.1850.651.6352.6955.5656.2756.8660.1861.6363.0663.7364.3465.8566.3766.9567.4868.2569.3169.8970.0370.8871.6972.9573.0274.4574.8575.5575.879.43

3-15.171.294.4111.0912.0419.4823.1226.7727.5728.05303132.332.3733.0233.6534.5836.3338.1840.2241.5443.5643.9244.7649.150.0450.651.8552.6854.2454.8655.1255.9656.5657.4458.558.658.9959.9860.460.7561.6662.262.362.5568.9970.2972.172.88

4.5-16.62-1.191.167.627.7411.1113.8217.0218.2418.6819.9821.3221.9922.222.4623.6123.7424.5926.1927.0629.4730.5530.9231.3635.736.7436.8238.2739.4439.8839.9241.4542.1842.4543.6644.1244.5944.8345.0245.8946.0746.3546.5946.8247.253.4754.6256.2156.61

6-16.01-1.220.585.365.555.897.7310.0110.6511.5612.8113.9214.0314.4314.7915.1716.4116.8217.2517.3719.4920.7520.8921.124.1324.9725.1725.9726.8527.4428.5229.7729.9230.2330.7931.4831.7231.8432.1332.4932.7432.8933.3333.5233.9138.6839.8241.0941.17

7.5-14.87-0.491.093.034.314.815.226.26.417.318.729.039.629.799.910.71111.7212.2612.6412.8414.2114.4514.5616.1816.7917.0217.0918.4219.5919.9621.1921.4121.4521.6922.4422.622.932323.0223.1723.2323.723.924.2727.4928.7329.2229.66

9-13.68-0.071.422.223.623.974.074.214.685.166.176.576.947.157.267.797.918.688.879.1510.0810.1710.310.4111.5611.611.7711.9613.0514.3114.4615.3615.6815.8315.8716.4516.616.7516.8316.8516.916.9317.2717.717.8320.1420.8221.6821.74

10.5-12.470.271.521.882.933.063.43.53.694.014.745.135.175.685.795.996.026.666.857.127.527.537.868.198.348.588.789.069.710.6810.8711.611.7612.1512.2612.4712.4812.5312.6212.6712.7912.9413.0813.3613.9215.1915.6116.4216.7

12-11.260.521.521.672.322.592.883.023.043.33.894.064.154.74.734.834.895.335.625.75.775.916.226.366.626.636.777.277.658.38.429.099.119.579.69.749.749.799.849.8610.0410.2810.3610.4511.1211.7512.1712.813.21

3/2+,T=3/2

1.514.1817.8320.5538.0840.242.7444.2244.8146.6448.2150.1951.2152.0952.9654.2854.9755.264.8966.7567.2267.5669.1769.4369.9270.7171.2571.7572.7275.8676.6577.3880.16

39.2412.2913.8129.5331.6732.934.0434.9735.9137.5538.8240.541.0641.5642.443.3343.3653.5954.6255.256.4257.4757.958.1358.8659.2559.9760.8662.0262.7363.2963.5275.5275.8376.4876.8177.9678.4278.979.9181.2282.6983.2584.3784.9294.9495.5195.9897.19

4.55.067.848.1620.1921.6422.3123.0323.9624.4425.3426.1327.6628.7129.1929.9430.6330.7839.340.1440.5542.7743.2943.6244.244.7244.9245.5546.3346.4446.7747.147.3359.6260.3260.4560.726262.5262.5763.364.2965.0165.366.0566.4278.1278.5778.8379.26

63.525.365.5613.2513.3514.3415.1315.9515.9916.9117.5517.718.2919.7620.4220.8921.0326.2927.4828.5130.2830.4830.9531.5432.1232.2332.4832.7832.9733.1133.3633.5743.7944.7444.9845.4845.946.6946.8647.1347.8848.0848.2148.6248.8260.4760.5660.8761.19

7.53.334.34.478.399.129.7110.0810.4111.1811.7311.9512.8513.2413.6613.7414.3614.4317.2918.5920.6721.2921.4521.7222.7422.8422.9623.0523.223.2523.3123.4924.2831.5832.4132.7133.2333.5133.9834.2334.534.934.934.9535.1535.2445.1245.3445.6845.92

93.13.693.85.86.746.987.167.28.38.58.549.629.8810.2310.2510.2610.5211.8212.9715.3315.4815.7815.9116.7116.7716.7916.8316.8616.9416.9917.0718.3623.223.8724.1624.4424.9525.0825.4325.5225.7125.7325.7425.8325.8633.733.9834.2834.45

10.52.743.183.244.365.15.225.35.756.496.586.627.177.57.667.678.28.388.569.4911.4711.8512.1212.1812.6912.7312.7412.7912.812.8512.8812.914.4417.5318.2718.4218.5818.919.319.3619.3819.4719.4919.5219.5719.625.7225.9526.2326.32

122.412.752.783.493.944.014.324.825.265.345.385.665.926.016.016.566.66.727.288.929.359.69.619.939.959.9810.0310.0510.0710.2410.3411.5713.6514.4714.514.614.915.1315.1615.1915.2215.2615.3115.3315.3420.1620.3420.5920.64

T=1/2

1.5-4.180.868.069.9713.1116.2928.3331.4233.843535.6436.0537.1437.6138.9739.4740.2340.9841.2341.8443.1643.844.4445.2346.0746.647.8450.3650.951.5551.8153.4754.6355.3457.2459.2261.2562.1562.9863.1463.363.5864.465.1765.9166.1366.7466.9567.6

3-8.21-2.43.75.499.6911.0820.0524.3525.2626.1926.3527.6428.6328.9130.431.1731.6431.8932.2232.5533.4333.7734.8935.1735.9536.4437.5139.3140.0640.8241.2442.3143.1643.3646.1447.9449.9350.450.751.5751.8352.4352.9353.2354.1554.5654.8555.6855.85

4.5-11.26-3.790.912.427.237.2711.8215.4516.1716.6817.2919.1619.6819.8420.7921.1221.6121.9822.5222.723.2423.7924.0724.1524.6425.8726.226.7127.352929.3929.930.4930.6133.2435.5336.6736.8136.8238.0738.3539.0839.4139.5940.5440.8941.0741.2541.77

6-12.5-2.830.521.695.285.757.748.459.549.8311.0512.0212.5813.3413.6213.7914.2514.6514.7715.1415.3215.7116.5116.5817.0617.1517.2317.5617.8219.4719.8120.0920.7120.8923.0324.3824.5125.0825.1926.1926.3927.2127.3728.1128.3128.7929.1229.5629.9

7.5-12.31-1.251.081.724.284.775.025.816.336.357.157.728.769.069.159.469.599.819.8410.7510.9511.0611.4811.6411.6812.1712.2512.6312.7212.8613.4813.8114.1914.4416.0416.1216.5916.9217.117.9818.0318.8619.5220.0520.1420.3320.4821.0421.16

9-11.44-0.271.411.623.613.733.914.074.644.955.15.856.076.736.846.896.947.067.187.938.028.298.58.658.658.88.889.119.5310.0710.0710.0810.1810.3811.1611.4611.6311.9411.9712.7212.7313.3314.4114.4614.7315.0715.2315.2715.42

10.5-10.40.231.521.572.863.053.113.483.683.883.994.634.664.95.175.455.475.635.756.026.076.426.666.676.736.836.847.17.257.527.717.8588.198.238.518.568.788.999.49.489.8210.7910.8711.0411.5311.5711.6911.92

12-9.350.511.521.542.252.582.73.013.033.163.293.743.773.854.064.444.54.684.734.774.815.185.335.375.395.545.625.695.835.96.146.226.396.446.596.626.636.777.017.277.367.728.428.428.569.069.099.269.42

5/2+

T=3/2

1.511.6715.6640.5941.31

37.9210.9331.6932.1178.4179.1880.0680.481.1881.9382.8284.3784.4695.5596.1

4.54.597.321.322.0462.5362.6563.3863.7564.0764.2665.1165.9866.1178.5378.85

63.385.3713.2314.6446.8346.8647.1247.2147.6147.8848.1648.5248.6560.4260.89

7.53.294.418.359.9933.9634.0734.4834.534.7734.9134.9435.0835.1645.0645.65

93.083.775.796.9724.9425.125.5125.5625.725.7225.7525.7825.8333.6934.24

10.52.733.224.365.118.8919.0419.3619.4519.4919.5119.5219.5219.5725.7226.19

122.412.773.483.9414.8814.8915.1315.2115.2215.2515.2615.2815.3120.1620.56

T=1/2

1.5-5.535.866.6810.32

3-8.692.53.68.05

4.5-11.330.491.736.64

6-12.510.421.535.56

7.5-12.311.051.694.7

9-11.441.411.613.68

10.5-10.41.511.563.09

12-9.351.521.542.7

CE2

00

00

00

00

00

00

00

00

taille

000

000

000

000

000

000

000

000

5H, 7/7/08

J=1/2+

J=3/2+

J=5/2+

0

0

0

1.5

1.5

1.5

0

0

0

0

0

0

3

3

3

0

0

0

0

0

0

4.5

4.5

4.5

0

0

0

0

0

0

6

6

6

0

0

0

0

0

0

7.5

7.5

7.5

0

0

0

0

0

0

9

9

9

0

0

0

0

0

0

10.5

10.5

10.5

0

0

0

0

0

0

12

12

12

0

0

0

0

0

0

11.0646

13.5237

11.0268

0

0

0

0

0

0

6.41955

8.6436

7.3352

0

0

0

0

0

0

2.40839

4.52705

4.0644

0

0

0

0

0

0

1.16383

3.04527

2.91063

0

0

0

0

0

0

1.46327

2.90087

2.85495

0

0

0

0

0

0

1.52493

2.69139

2.67282

0

0

0

0

0

0

1.31336

2.35808

2.35024

0

0

0

0

0

0

1.10711

2.04498

2.04149

0

0

0

CE

1/2+0010000

2010001

2210110

2211110

2231110

2232110

4010002

4010220

4011220

4210111

4211111

4231111

4232111

4232130

6010003

6010221

6011221

6210112

6211112

6231112

6232112

6232131

8010004

8010222

8011222

8210113

8211113

8231113

8232113

8232132

10010005

10010223

10011223

10210114

10211114

10231114

10232114

10232133

12010006

12010224

12011224

12210115

12211115

12231115

12232115

12232134

3/2+2012020

2012200

2211110

2212110

2230110

2231110

2232110

4011220

4012021

4012201

4012220

4211111

4212111

4212130

4230111

4231111

4232111

4232130

4233130

6011221

6012022

6012202

6012221

6012240

6211112

6212112

6212131

6230112

6231112

6232112

6232131

6233131

8011222

8012023

8012203

8012222

8012241

8211113

8212113

8212132

8230113

8231113

8232113

8232132

8233132

10011223

10012024

10012204

10012223

10012242

10211114

10212114

10212133

10230114

10231114

10232114

10232133

10233133

12011224

12012025

12012205

12012224

12012243

12211115

12212115

12212134

12230115

12231115

12232115

12232134

12233134

5/2+2012020

2012200

2212110

2231110

2232110

4012021

4012201

4012220

4013220

4212111

4212130

4213130

4231111

4232111

4232130

4233130

4234130

6012022

6012202

6012221

6012240

6013221

6013240

6212112

6212131

6213131

6231112

6232112

6232131

6233131

6234131

6234150

8012023

8012203

8012222

8012241

8013222

8013241

8212113

8212132

8213132

8231113

8232113

8232132

8233132

8234132

8234151

10012024

10012204

10012223

10012242

10013223

10013242

10212114

10212133

10213133

10231114

10232114

10232133

10233133

10234133

10234152

12012025

12012205

12012224

12012243

12013224

12013243

12212115

12212134

12213134

12231115

12232115

12232134

12233134

12234134

12234153

1/2+,T=1/2

0010000

0210000

2010001

2010110

2011110

2210001

2210110

2211110

2231110

2232020

2232110

2232200

4010002

4010111

4010220

4011111

4011220

4210002

4210111

4210220

4211111

4211220

4231111

4231220

4232021

4232111

4232130

4232201

4232220

6010003

6010112

6010221

6011112

6011221

6210003

6210112

6210221

6211112

6211221

6231112

6231221

6232022

6232112

6232131

6232202

6232221

6232240

8010004

8010113

8010222

8011113

8011222

8210004

8210113

8210222

8211113

8211222

8231113

8231222

8232023

8232113

8232132

8232203

8232222

8232241

10010005

10010114

10010223

10011114

10011223

10210005

10210114

10210223

10211114

10211223

10231114

10231223

10232024

10232114

10232133

10232204

10232223

10232242

12010006

12010115

12010224

12011115

12011224

12210006

12210115

12210224

12211115

12211224

12231115

12231224

12232025

12232115

12232134

12232205

12232224

12232243

3/2+,T=1/2

0230000

2011110

2012020

2012110

2012200

2211110

2212020

2212110

2212200

2230001

2230110

2231110

2232020

2232110

2232200

4011111

4011220

4012021

4012111

4012130

4012201

4012220

4211111

4211220

4212021

4212111

4212130

4212201

4212220

4230002

4230111

4230220

4231111

4231220

4232021

4232111

4232130

4232201

4232220

4233130

4233220

6011112

6011221

6012022

6012112

6012131

6012202

6012221

6012240

6211112

6211221

6212022

6212112

6212131

6212202

6212221

6212240

6230003

6230112

6230221

6231112

6231221

6232022

6232112

6232131

6232202

6232221

6232240

6233131

6233221

6233240

8011113

8011222

8012023

8012113

8012132

8012203

8012222

8012241

8211113

8211222

8212023

8212113

8212132

8212203

8212222

8212241

8230004

8230113

8230222

8231113

8231222

8232023

8232113

8232132

8232203

8232222

8232241

8233132

8233222

8233241

10011114

10011223

10012024

10012114

10012133

10012204

10012223

10012242

10211114

10211223

10212024

10212114

10212133

10212204

10212223

10212242

10230005

10230114

10230223

10231114

10231223

10232024

10232114

10232133

10232204

10232223

10232242

10233133

10233223

10233242

12011115

12011224

12012025

12012115

12012134

12012205

12012224

12012243

12211115

12211224

12212025

12212115

12212134

12212205

12212224

12212243

12230006

12230115

12230224

12231115

12231224

12232025

12232115

12232134

12232205

12232224

12232243

12233134

12233224

12233243

J=5/2+2012020

2012110

2012200

2212020

2212110

2212200

2231110

2232020

2232110

2232200

4012021

4012111

4012130

4012201

4012220

4013130

4013220

4212021

4212111

4212130

4212201

4212220

4213130

4213220

4231111

4231220

4232021

4232111

4232130

4232201

4232220

4233130

4233220

4234040

4234130

4234220

6012022

6012112

6012131

6012202

6012221

6012240

6013131

6013221

6013240

6212022

6212112

6212131

6212202

6212221

6212240

6213131

6213221

6213240

6231112

6231221

6232022

6232112

6232131

6232202

6232221

6232240

6233131

6233221

6233240

6234041

6234131

6234150

6234221

6234240

8012023

8012113

8012132

8012203

8012222

8012241

8013132

8013222

8013241

8212023

8212113

8212132

8212203

8212222

8212241

8213132

8213222

8213241

8231113

8231222

8232023

8232113

8232132

8232203

8232222

8232241

8233132

8233222

8233241

8234042

8234132

8234151

8234222

8234241

8234260

10012024

10012114

10012133

10012204

10012223

10012242

10013133

10013223

10013242

10212024

10212114

10212133

10212204

10212223

10212242

10213133

10213223

10213242

10231114

10231223

10232024

10232114

10232133

10232204

10232223

10232242

10233133

10233223

10233242

10234043

10234133

10234152

10234223

10234242

10234261

12012025

12012115

12012134

12012205

12012224

12012243

12013134

12013224

12013243

12212025

12212115

12212134

12212205

12212224

12212243

12213134

12213224

12213243

12231115

12231224

12232025

12232115

12232134

12232205

12232224

12232243

12233134

12233224

12233243

12234044

12234134

12234153

12234224

12234243

12234262

energies

K=0K=2,n=1n=0,S12=1,S=1,l=1,L=0n=0,S12=1,S=1,l=1,L=1n=0,S12=1,S=3,l=1,L=1n=0,S12=1,S=3,l=1,L=2

1/2+1.514.5713.4446.6223.3720.1649.8548.0145.6542.3446.1254.7955.5147.7950.7269.8165.9169.3969.7974.5574.7475.6367.8693.288.1189.9791.697.4298.1698.4887.3484.56103.8788.02115.5120.17121.22121.2497.2414.0723.8214.8739.5632.8426.025.7720.51

314.587.6738.1315.1713.3938.3237.2335.3232.5435.1843.1243.4236.8739.1257.6954.357.9957.6462.0462.2361.9656.4179.875.5877.8378.8283.6184.1184.0975.54101.1796.8797.9398.5104.45105.17105.9995.27121.51116.28118.26119.23125.28126.18128.33114.47

4.5143.4729.798.357.9825.5325.4124.1721.7623.1930.4330.3525.0726.4542.5439.8843.7642.6346.4846.6745.6142.0961.9558.9861.761.9165.4965.7465.4259.6481.9779.0680.1179.9884.6885.1384.9478.37101.2697.0799.3199.73104.15104.72105.9596.74

69.442.5321.985.145.315.9516.6417.113.9614.6720.620.4516.5417.429.3327.4831.2129.7232.7632.8931.8429.6144.8343.146.0945.7148.1848.2847.8344.1762.1660.7861.861.0764.5864.8264.0860.6479.3376.4878.8678.8681.7582.0782.677.22

7.55.572.8515.263.974.1310.1811.313.989.429.9513.9913.911.5312.1120.2719.1122.2320.812323.0622.2820.9431.7130.9233.7333.1834.7234.7634.3932.0845.6145.4646.3445.2847.8747.9847.1245.559.8958.2860.6360.3562.1362.2862.4559.52

93.462.8610.533.343.446.918.211.966.927.479.849.818.68.9714.6113.9816.2215.1216.6416.6616.0915.4222.8422.624.9724.5325.3625.3825.1923.6833.5634.1534.7533.6535.635.6534.8634.1544.8544.1446.2845.9346.9847.0547.0945.49

10.52.362.577.492.822.874.986.289.995.476.037.287.276.716.9611.0310.8212.2111.4512.4812.4912.111.8617.0717.0918.9518.719.0819.0919.031825.2926.2326.5225.5227.0327.0626.426.1134.0433.8535.7235.433636.0436.0635.14

121.752.245.552.392.423.785.018.24.515.045.645.645.395.588.668.749.499.029.699.79.449.4613.2413.3814.7914.6914.8114.8214.8314.119.6420.6820.7419.8821.0721.0820.5620.4626.4526.5228.127.9128.228.2228.2427.67

S12=0,S=1,L=2,lx=0,ly=2S12=0,S=1,L=2,lx=2,ly=0S12=1,S=1,L=1,lx=1,ly=1S12=1,S=1,L=2,lx=1,ly=1S12=1,S=3,L=0,lx=1,ly=1S12=1,S=3,L=1,lx=1,ly=1S12=1,S=3,L=2,lx=1,ly=1

3/2+1.514.9215.0919.7552.1842.8117.9248.8741.2443.7544.2250.6851.5149.2650.642.1953.6146.6649.2351.9768.7269.3570.5368.7568.7470.8875.0970.0367.6772.8174.0868.1674.0489.6192.7590.3491.1889.2192.8597.1389.7490.2795.8296.4688.5395.6187.73126.9102.27305.34

39.6211.7513.2740.3735.3212.237.7831.7933.8635.0940.4341.338.0339.2732.1342.3536.2638.1340.9457.5156.8959.2557.5356.9259.6861.8558.1655.8660.9960.9956.661.5977.5679.4278.0878.7476.6980.4683.1677.4777.7582.582.6776.482.3397.75100.7299.0799.06

4.55.6910.977.6927.0127.837.5625.3421.3723.0224.7829.0629.7225.6826.7121.3529.9424.8725.9628.7443.4941.5445.0343.3742.245.3645.843.2841.3146.0845.1642.1946.1161.5561.7161.7262.1460.0763.7864.9161.0261.264.8764.6360.1664.7879.9981.581.0781.04

64.779.844.9416.8620.515.1715.913.7915.2216.8120.3220.3716.717.5613.920.3116.4817.2119.3431.0928.4632.2630.7129.4632.3232.0630.2628.8932.6631.6629.6532.4846.0144.7245.7846.0344.0947.447.645.0645.3147.8847.4644.4447.8461.7361.7562.4962.44

7.54.577.733.9110.7214.194.0910.179.3410.811.7714.4813.9111.5212.159.7413.8511.5212.0413.2522.1819.622.9221.6520.722.8422.4121.2220.3822.9722.220.9622.7633.731.7433.233.3531.7534.3934.332.6132.9734.5934.2332.2234.646.345.346.7946.71

93.915.823.327.249.793.426.96.888.258.6810.689.818.578.987.459.798.598.949.4916.214.116.6815.7815.1416.5716.1415.5214.9216.6216.0615.4216.4224.9522.9824.3824.4723.3225.2125.1623.9724.4225.325.1223.7525.3634.7433.3235.0735

10.53.194.432.815.26.992.874.985.456.546.698.157.276.696.976.047.276.716.957.1212.210.6412.5811.9811.5712.4512.1111.9111.3812.4712.0811.8712.318.9517.2418.4218.4817.7419.0119.0218.1518.6419.0518.9918.0319.1126.5225.1126.7926.73

122.613.482.383.935.192.413.774.55.35.356.415.645.395.595.045.645.395.575.569.498.379.829.429.189.689.449.4999.699.439.469.5614.7913.4114.3514.3913.9814.7714.8314.1714.6514.814.8114.1114.8520.7319.520.9720.93

5/2+S12=0,S=1,L=2,lx=0,ly=2S12=0,S=1,L=2,lx=2,ly=0S12=1,S=1,L=2,lx=1,ly=1S12=1,S=3,L=1,lx=1,ly=1S12=1,S=3,L=2,lx=1,ly=1

1.513.5113.6449.3814.1947.2243.4744.1249.9444.7145.5947.3551.9150.4344.7746.7550.950.6369.3270.4468.4967.1571.8370.1369.971.3973.8569.5971.568.6873.3272.873.4992.7790.2991.0788.891.7390.9190.493.7395.2691.9293.190.5294.9895.7491127.11102.11

38.8810.9138.8410.2236.8833.7135.0639.9635.5836.0337.0540.9840.5735.2536.4740.3639.4856.959.1957.3955.7660.3158.6458.6259.0461.5458.9259.3956.9361.1560.160.9879.4478.0578.6876.479.4778.5378.4480.3382.0979.8180.3277.8581.9181.4578.42100.7399.05

4.55.4410.6726.476.8625.0222.9624.7928.8624.9824.9725.5828.7929.2524.5225.1528.5327.4241.584543.3241.5345.7744.2144.2943.7146.1645.0944.4142.3545.9144.6145.4461.7161.7162.1259.963.1262.0362.2962.6964.6463.463.3261.0264.5663.0461.5481.581.06

64.79.7616.724.9615.8215.216.8220.2616.6516.5117.119.3620.0916.3916.8919.2818.5628.4932.2530.729.1432.731.4131.4630.4332.5532.2831.3629.7232.4131.3331.9244.7245.7846.024447.0546.0246.3745.947.7747.2146.8544.8847.7545.9245.2461.7562.49

7.54.557.7110.694.0210.1510.811.7814.4611.5211.4711.9713.2513.7811.4911.9113.2313.0619.6222.9121.6520.5523.122.2222.1721.2922.822.8322.0820.9822.7322.1622.4231.7333.233.3531.7134.2733.4433.7733.0234.5634.333.9732.4334.5632.9932.6345.346.79

93.95.817.233.396.98.258.6810.678.498.558.99.489.768.588.899.489.6314.1116.6815.7815.0816.6716.1516.0415.5516.4316.5616.0115.4416.4116.316.2622.9724.3824.4723.325.2324.6124.9224.1725.3525.182523.8625.3424.1623.9733.3335.07

10.53.184.435.22.854.976.546.698.156.566.686.937.117.256.76.927.127.3710.6512.5811.9811.5412.4612.1612.0611.9212.312.4512.0611.8712.312.4812.2517.2418.4218.4817.7319.0718.6118.9118.2519.1118.9918.9418.0919.118.2618.1925.1126.79

122.613.483.932.413.775.35.356.415.245.395.575.555.635.395.565.565.828.379.829.429.169.669.479.429.59.559.679.429.469.569.869.5513.414.3514.3913.9814.8414.4914.7814.2214.8514.7714.7914.1514.8414.2614.2619.520.97

energies

000000

000000

000000

000000

000000

000000

000000

000000

K=0

K=2,n=1

n=0,S12=1,S=1,l=1,L=0

n=0,S12=1,S=1,l=1,L=1

n=0,S12=1,S=3,l=1,L=1

n=0,S12=1,S=3,l=1,L=2

Feuil1 (2)

0000000

0000000

0000000

0000000

0000000

0000000

0000000

0000000

S12=0,S=1,L=2,lx=0,ly=2

S12=0,S=1,L=2,lx=2,ly=0

S12=1,S=1,L=1,lx=1,ly=1

S12=1,S=1,L=2,lx=1,ly=1

S12=1,S=3,L=0,lx=1,ly=1

S12=1,S=3,L=1,lx=1,ly=1

S12=1,S=3,L=2,lx=1,ly=1

vb

00000

00000

00000

00000

00000

00000

00000

00000

S12=0,S=1,L=2,lx=0,ly=2

S12=0,S=1,L=2,lx=2,ly=0

S12=1,S=1,L=2,lx=1,ly=1

S12=1,S=3,L=1,lx=1,ly=1

S12=1,S=3,L=2,lx=1,ly=1

juin08

rdia4_H5.OK

Parameter=1.12Energie,largeur=4.28E+001.68E+00

Parameter=1.12Energie,largeur=2.09E+006.63E-01


Parameter=1.12Energie,largeur=1.65E+00-1.07E+00






rdia_H5.OK2



Parameter=1.12Energie,largeur=1.50E+00-6.37E-01







resdia_H5








rdia_H5_32.OK



Parameter=1.12Energie,largeur=5.54E-01-2.53E+00


Parameter=1.12Energie,largeur=-3.00E-01-3.24E+00





resdia_32.OK



Parameter=1.12Energie,largeur=5.54E-01-2.53E+00


Parameter=1.12Energie,largeur=-3.00E-01-3.24E+00





rdia5_He5.OK:Parameter=1.12Energie,largeur=4.85E+001.83E+00

rdia5_He5.OK:Parameter=1.12Energie,largeur=2.78E+001.14E+00

rdia5_He5.OK:Parameter=1.12Energie,largeur=1.99E+00-3.56E-01







rdia5_He5.OK2:Parameter=1.12Energie,largeur=4.85E+001.83E+00

rdia5_He5.OK2:Parameter=1.12Energie,largeur=2.78E+001.14E+00

rdia5_He5.OK2:Parameter=1.12Energie,largeur=1.99E+00-3.56E-01







res_He5.OK:Parameter=1.12Energie,largeur=5.23E+001.46E+00

res_He5.OK:Parameter=1.12Energie,largeur=2.80E+009.11E-01

res_He5.OK:Parameter=1.12Energie,largeur=1.80E+00-5.72E-01







res_He5.OK2:Parameter=1.12Energie,largeur=5.16E+001.56E+00

res_He5.OK2:Parameter=1.12Energie,largeur=2.80E+001.04E+00

res_He5.OK2:Parameter=1.12Energie,largeur=1.95E+00-4.25E-01







juin08

000000

000000

000000

000000

000000

000000

000000

0000

0000

Trento

0000

0000

0000

0000

0000

0000

0000

0000

0000

figs

00000000

00000000

00000000

00000000

00000000

00000000

00000000

00000000

00000000

Feuil1

amq=1.62619775271.63869775271.65119775271.66369775272.12619775272.15119775272.17619775272.20119775272.22619775272.25119775272.27619775272.30119775272.32619775272.35119775272.37619775272.40119775272.42619775272.45119775272.4761977527

11.12Energie,largeur=4.28E+001.68E+00rdia2

21.12Energie,largeur=2.09E+006.63E-01

31.12Energie,largeur=1.98E+00-1.93E-01

41.12Energie,largeur=1.65E+00-1.09E+00






pm1 pdesc]$ grep ' 1.1200'rdia


21.12Energie,largeur=2.00E+001.27E+00

















1 8

2 1 1 25.00000000000000 12 0 0 20 1

3 1.000000000000000E-08 100.0000000000000 0.000000000000000E+00 -10

4 5 1.625000000000000 1.000000000000000E-02

5 /nobackup/pdesc/H5_He5/H5_hydra

1701 6 0.000000000000000E+00 1.250000000000000E-02

1702 15 7.500000000000000E-02 3.000000000000000E-02

calculs etats liesPad

1.122.121Parameter=1.12Energie,largeur=1.65E+00-1.07E+00

1.221.875Parameter=1.22Energie,largeur=1.71E+00-6.46E-01



1.520.842Parameter=1.52Energie,largeur=8.49E-01-1.32E-02

1.620.065

Feuil1

000000

000000

000000

000000

000000

000000

000000

000000

000000

He5

im=11.6261977527-6.64E-080.00E+002.58E-04N=61.121.65158936470.24789364091.6261887898-0-0

im=21.6511977527-0.25695725870.1581138830.506909517201.221.70548213160.1156850721.6311887898-0.0493587288-0.0000001399

im=31.6761977527-0.54009713280.22360679770.73491301040.00000231711.321.5982514410.03341947811.6361887898-0.0997228248-0.0000002808

im=41.7011977527-0.85050822790.27386127880.92223002983.12554050071.421.32036409920.00296226091.6411887898-0.1511035351-0.0000004228

im=51.7261977527-1.18900808830.3162277661.090416474710423.28758716581.520.834259499-0.00036532411.6461887898-0.2035117233-0.0000005657

im=61.7511977527-1.55612651370.35355339061.2474480004-15922.20282363891.620.0597190615-0.00000005671.6511887898-0.2569578571-0.0000007097

im=71.7761977527-1.95211889990.38729833461.397182486329098.8693046571.72-1.1025600271.6561887898-0.3114519966-0.0000008546

im=81.8011977527-2.37698764010.41833001331.5417482415-12130.20132732391.82-2.71558569051.6861887898-0.6609345503-0.0000017428

im=91.8261977527-2.83051074390.44721359551.682412180219344.15397262571.92-4.77900493071.7161887898-1.0501950733-0.0000026546

0.1935266152101.8511977527-3.30330783090.4743416491.81750043493334.35955691341.7461887898-1.4803945972-0.0000035765

im=111.8761977527-3.81307616040.51.952709953-5094.24776363371.7761887898-1.9521153305-0.0000044942

im=121.9011977527-4.34983047770.52440442412.08562472125914.16854810721.8061887898-2.4654057661-0.0000053927

im=131.9261977527-4.91277004980.54772255752.21647694551336.84651243691.8361887898-3.0198497019-0.0000062572

im=141.9511977527-5.50102452390.57008771252.345426299-1049.8619762659

im=151.9761977527-6.11368017760.59160797832.47258572711411.4384704828

im=162.0011977527-6.74979889320.61237243572.598037508-617.6780523062

im=172.0261977527-7.40843438020.6324555322.7218439302355.5733721256

im=182.0511977527-8.08761175740.65192024052.843872669-86.1644617319

im=192.0761977527-8.77667733530.67082039322.9625457524-20.9965118654

im=202.1011977527-9.49776329470.68920243763.081844138614.4596276581

im=212.1261977527-10.23770665530.70710678123.19964164486.7867104557

im=222.1511977527-10.99566021210.72456883733.3159704782-195.5105438232

im=232.1761977527-11.77081171480.74161984873.430861657863.763961792

im=242.2011977527-12.56238495020.75828754443.5443454897

im=252.2261977527-13.36964014410.77459666923.6564518517

im=262.2511977527-14.19181780720.7905694153.7672029156

im=272.2761977527-15.02835895730.80622577483.8766427431

resdia:im=11.6261977459-3.16E-120.00E+001.78E-06

resdia:im=21.6311977459-4.94E-027.07E-020.2221678976

resdia:im=31.6361977459-9.97E-020.10.3157887364

resdia:im=41.6411977459-0.15110310140.12247448710.3887198238

resdia:im=51.6461977459-0.20351116510.14142135620.4511221178

resdia:im=61.6511977459-0.25695718530.1581138830.5069094449

resdia:im=71.6561977459-0.31145122250.17320508080.5580781509

resdia:im=81.6861977459-0.66093656220.24494897430.8129800503

resdia:im=91.7161977459-1.05019717410.31.0247912832

resdia:im=101.7461977459-1.48039717710.34641016151.2167157339

resdia:im=111.7761977459-1.95211878830.38729833461.3971824463

resdia:im=121.8061977459-2.46541048540.42426406871.5701625666

resdia:im=131.8361977459-3.01985603130.45825756951.7377732969

resdia:im=141.8661977459-3.60588829270.48989794861.8989176635

resdia:im=151.8961977459-4.24035775290.51961524232.0592128965

resdia.bak:im=11.6261887898-5.37E-120.00E+002.32E-06

resdia.bak:im=21.6311887898-4.94E-027.07E-020.2221679295

resdia.bak:im=31.6361887898-9.97E-020.10.3157887649

resdia.bak:im=41.6411887898-0.15110311230.12247448710.3887198379

resdia.bak:im=51.6461887898-0.20351115760.14142135620.4511221094

resdia.bak:im=61.6511887898-0.25695714740.1581138830.5069094075

resdia.bak:im=71.6561887898-0.3114511420.17320508080.5580780788

resdia.bak:im=81.6861887898-0.66093280750.24494897430.8129777411

resdia.bak:im=91.7161887898-1.05019241870.31.024788963

resdia.bak:im=101.7461887898-1.48039102070.34641016151.2167132039

resdia.bak:im=111.7761887898-1.95211083630.38729833461.3971796006

resdia.bak:im=121.8061887898-2.46540037350.42426406871.5701593465

resdia.bak:im=131.8361887898-3.01984344470.45825756951.7377696754

resdia.bak:im=141.8661887898-3.61463971610.48989794861.9012205859

resdia.bak:im=1.50E+011.90E+00-4.25E+005.20E-012.0612344029

im=162.1486325379-8.87965970290.58736700622.9798757865

im=172.1786325379-9.89354447720.61237243573.1454005273

im=182.2086325379-10.93471952180.63639610313.3067687433

im=192.2386325379-12.00150888080.65954529793.4643193965

12/6/08

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

He5

000000

000000

000000

000000

000000

000000

00000

00000

00000

0000

0000

0000

0000

0000

0000

0

0

0

0

0

0

0

Feuil3

K=0K=2

1.514.57513.43746.62223.36820.15749.85348.01445.65442.3446.119

314.5837.66738.12815.16713.39238.31637.22735.32332.54435.184

4.514.0033.46729.7948.3527.98225.53325.41124.17221.76223.185

69.4422.5321.9835.1365.29615.95216.63717.09613.9614.668

7.55.5752.85215.2623.9724.13510.18411.29613.9759.4169.945

93.4572.86110.5313.3423.4376.9088.19811.966.9167.473

10.52.3592.5717.4922.8232.8744.9786.2849.9915.4656.034

121.7522.2385.552.3892.4183.7755.0158.1994.5145.044

Kmax=12Kmax=8Kmax=4Kmax=2

1.51.11E+011.11E+011.11E+011.16E+01

36.42E+006.44E+006.54E+006.86E+00

4.52.41E+002.42E+002.64E+002.84E+00

61.16E+001.19E+001.50E+001.68E+00

7.51.46E+001.55E+001.90E+002.03E+00

91.52E+001.65E+001.94E+002.04E+00

10.51.31E+001.42E+001.60E+001.74E+00

121.11E+001.19E+001.29E+001.43E+00

Kmax=12Kmax=8Kmax=4Kmax=2

1.51.35E+011.35E+011.37E+011.40E+01

38.64E+008.65E+008.87E+009.10E+00

4.54.53E+004.53E+004.78E+004.97E+00

63.05E+003.06E+003.33E+003.51E+00

7.52.90E+002.95E+003.21E+003.34E+00

92.69E+002.76E+002.98E+003.05E+00

10.52.36E+002.43E+002.59E+002.64E+00

122.04E+002.11E+002.22E+002.25E+00

K=2K=2bK=2c

1.514.91615.09419.74952.18142.80617.91948.86641.24343.75344.21

39.62111.74713.26840.36535.31712.20237.77831.7933.86335.09

4.55.6910.9697.69427.01227.8327.56325.34221.36823.01824.78

64.7669.844.94116.85720.5055.1715.90313.78715.21716.81

7.54.577.7293.90510.72314.1924.09210.1729.34110.80211.76

93.915.8223.3157.2449.7943.4196.9046.8818.2558.67

10.53.1884.4342.815.26.9852.8664.9775.4486.5416.69

122.6123.4782.3833.9295.1932.4143.7754.5055.35.34

Kmax=12kmax=8kmax=4kmax=2

1.51.10E+011.10E+011.13E+011.18E+01

37.34E+007.35E+007.70E+008.09E+00

4.54.06E+004.07E+004.42E+004.68E+00

62.91E+002.93E+003.24E+003.43E+00

7.52.85E+002.90E+003.19E+003.32E+00

92.67E+002.74E+002.97E+003.04E+00

10.52.35E+002.42E+002.59E+002.63E+00

122.04E+002.11E+002.22E+002.25E+00

1.513.51213.64249.37814.18947.2243.47444.12349.93544.71545.585

38.87710.91138.83810.21836.8833.71135.06139.96135.58436.028

4.55.44410.66926.476.86425.02522.96224.78628.86324.9824.974

64.7039.7616.7164.96115.82115.19916.82520.25616.65116.508

7.54.5517.70710.6874.01910.15110.79611.77614.46411.51911.468

93.9035.8147.2333.396.8978.2538.68210.6738.4918.55

10.53.1844.435.1962.8524.9746.546.6938.1486.5626.683

122.6113.4773.9272.4073.7745.2995.3476.4095.2435.385

Feuil3

00000000000

00000000000

00000000000

00000000000

00000000000

00000000000

00000000000

00000000000

Kmax=12

Kmax=8

Kmax=4

Kmax=2

Feuil4

00000000000

00000000000

00000000000

00000000000

00000000000

00000000000

00000000000

00000000000

Kmax=12

Kmax=8

Kmax=4

Kmax=2

Feuil5

0000

0000

0000

0000

0000

0000

0000

0000

J=1/2+

J=3/2+

K=2

K=2b

K=2c

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Kmax=12

Kmax=8

Kmax=4

Kmax=2

0000

0000

0000

0000

0000

0000

0000

0000

J=5/2+

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

Kmax=12

kmax=8

kmax=4

kmax=2

0000

0000

0000

0000

0000

0000

0000

0000

Kmax=12

Kmax=8

Kmax=4

Kmax=2

J=1/2+J=3/2+J=5/2+J=1/2-1/2+,T=3/23/2+,T=3/2

1.51.11E+011.35E+011.10E+012.79E+011.17E+011.20E+011.42E+011.44E+01

36.42E+008.64E+007.34E+002.00E+017.01E+007.26E+009.24E+009.49E+00

4.52.41E+004.53E+004.06E+001.13E+012.93E+003.18E+005.06E+005.31E+00

61.16E+003.05E+002.91E+005.69E+001.63E+001.88E+003.52E+003.77E+00

7.51.46E+002.90E+002.85E+003.08E+001.89E+002.14E+003.33E+003.58E+00

91.52E+002.69E+002.67E+002.08E+001.92E+002.17E+003.10E+003.35E+00

10.51.31E+002.36E+002.35E+001.67E+001.69E+001.94E+002.74E+002.99E+00

121.11E+002.04E+002.04E+001.43E+001.47E+001.72E+002.41E+002.66E+00

13.83E+002.07E+00

22.00E+001.27E+00

31.65E+00-1.15E+00

41.74E+00-9.70E-01

51.67E+00-1.08E+00

61.68E+00-1.07E+00

71.53E+00-1.72E+00

81.59E+00-1.50E+00

91.54E+00-1.63E+00

101.55E+00-1.62E+00

111.54E+00-1.63E+00

im=11.63E+00-6.63E-080.00E+002.57E-04

im=21.65E+00-2.57E-011.58E-015.07E-01

im=31.6761917686-0.54009667310.22360679770.7349126976

im=41.7011917686-0.85050728220.27386127880.9222295171

im=51.7261917686-1.18900649180.3162277661.0904157426

im=61.7511917686-1.55612411780.35355339061.2474470401

im=71.7761917686-1.95211558020.38729833461.3971812982

im=81.8011917686-2.37698330290.41833001331.5417468349

im=91.8261917686-2.83050532930.44721359551.682410571

im=101.8511917686-3.30330544350.4743416491.8174997781

im=111.8761917686-3.81307272710.51.9527090739

im=121.9011917686-4.34982601940.52440442412.0856236524

im=131.9261917686-4.9127646250.54772255752.2164757217

im=141.9511917686-5.50101821180.57008771252.3454249534

im=151.9761917686-6.11367307880.59160797832.4725842915

im=162.0011917686-6.74979112460.61237243572.598036013

im=172.0261917686-7.40842607150.6324555322.7218424039

im=182.0511917686-8.08760286130.65192024052.8438711049

im=192.0761917686-8.77680821490.67082039322.9625678414

im=202.1011917686-9.49789216560.68920243763.0818650466

im=212.1261917686-10.23783350110.70710678123.1996614666

im=222.1511917686-10.9957850450.72456883733.3159893011

im=232.1761917686-11.77093457060.74161984873.4308795622

im=242.2011917686-12.56250588420.75828754443.5443625498

im=252.2261917686-13.36975922660.77459666923.6564681356

im=262.2511917686-14.19193511530.7905694153.7672184852

im=272.2761917686-15.02847458620.80622577483.8766576566

H5, u=1.12 le 17/12/2007

0000

0000

0000

0000

0000

0000

0000

0000

J=1/2+

J=3/2+

J=5/2+

J=1/2-

R (fm)

E (MeV)

5H

00

00

00

00

00

00

00

00

00

00

00

Er

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

u0=1.62

u=1.12

u

E (MeV)

0000

0000

0000

0000

0000

0000

0000

0000

J=1/2+

J=3/2+

J=1/2+

J=3/2+

1/2+,T=3/2

3/2+,T=3/2

R (fm)

E (MeV)

5H, 5He

Parameter=1.1214.67E+002.2982

Parameter=1.1222.11E+000.759

Parameter=1.1231.81E+00-0.4584

Parameter=1.1241.81E+00-0.4584

Parameter=1.1251.79E+00-0.4802

Parameter=1.1261.80E+00-0.474

Parameter=1.1271.96E+00-0.4764

Parameter=1.1281.95E+00-0.472

Parameter=1.1292.00E+00-0.5356

Parameter=1.12101.96E+00-0.487

Parameter=1.12112.20E+00-0.8442

14.5713.4423.3720.1649.85

14.587.6715.1713.3938.32

143.478.357.9825.53

9.442.535.145.315.95

5.572.853.974.1310.18

3.462.863.343.446.91

2.362.572.822.874.98

1.752.242.392.423.78

(a) lx=0, ly=0, L=0, Sbc=0, S=1/2(b) lx=0, ly=0, L=0, Sbc=1, S=1/2(c) lx=1, ly=1, L=1, Sbc=1, S=1/2(d) lx=1, ly=1, L=1, Sbc=1, S=3/2 (e) lx=1, ly=1, L=2, Sbc=1, S=3/2

(a)

(d)

(c)

(e)

(b)

J=1/2+

K=0

K=2,n=1

n=0,S12=1,S=1,l=1,L=1

n=0,S12=1,S=3,l=1,L=1

n=0,S12=1,S=3,l=1,L=2

14.9215.0919.7517.9248.87

9.6211.7513.2712.237.78

5.6910.977.697.5625.34

4.779.844.945.1715.9

4.577.733.914.0910.17

3.915.823.323.426.9

3.194.432.812.874.98

2.613.482.382.413.77

J=3/2+

(a) lx=0, ly=2, L=2, Sbc=0, S=1/2(b) lx=2, ly=0, L=2, Sbc=0, S=1/2 (c) lx=1, ly=1, L=1, Sbc=1, S=1/2 (d) lx=1, ly=1, L=1, Sbc=1, S=3/2 (e) lx=1, ly=1, L=2, Sbc=1, S=3/2

(e)

(d)

(c)

(b)

(a)

S12=0,S=1,L=2,lx=0,ly=2

S12=0,S=1,L=2,lx=2,ly=0

S12=1,S=1,L=1,lx=1,ly=1

S12=1,S=3,L=1,lx=1,ly=1

S12=1,S=3,L=2,lx=1,ly=1

13.5113.6449.3814.19

8.8810.9138.8410.22

5.4410.6726.476.86

4.79.7616.724.96

4.557.7110.694.02

3.95.817.233.39

3.184.435.22.85

2.613.483.932.41

J=5/2+

(a) lx=0, ly=2, L=2, Sbc=1, S=1/2(b) lx=2, ly=0, L=2, Sbc=0, S=1/2(c) lx=1, ly=1, L=2, Sbc=1, S=1/2(d) lx=1, ly=1, L=1, Sbc=1, S=3/2

(d)

(c)

(b)

(a)

S12=0,S=1,L=2,lx=0,ly=2

S12=0,S=1,L=2,lx=2,ly=0

S12=1,S=1,L=2,lx=1,ly=1

S12=1,S=3,L=1,lx=1,ly=1

11.7214.1811.6711.064613.523711.0268-11.79-4.18-5.53

7.019.247.926.419558.64367.3352-15.17-8.21-8.69

2.935.064.592.408394.527054.0644-16.62-11.26-11.33

1.633.523.381.163833.045272.91063-16.01-12.5-12.51

1.893.333.291.463272.900872.85495-14.87-12.31-12.31

1.923.13.081.524932.691392.67282-13.68-11.44-11.44

1.692.742.731.313362.358082.35024-12.47-10.4-10.4

1.472.412.411.107112.044982.04149-11.26-9.35-9.35

E(R) (MeV)

R (fm)

1/2-

5/2+

3/2+

1/2+

J=1/2+

J=3/2+

J=5/2+

J=1/2-

R (fm)

E(R) (MeV)

5H

1.5

1.5

1.5

1.5

3

3

3

3

4.5

4.5

4.5

4.5

6

6

6

6

7.5

7.5

7.5

7.5

9

9

9

9

10.5

10.5

10.5

10.5

12

12

12

12

11.0646

13.5237

11.0268

27.878

6.41955

8.6436

7.3352

20.0437

2.40839

4.52705

4.0644

11.3488

1.16383

3.04527

2.91063

5.69138

1.46327

2.90087

2.85495

3.07553

1.52493

2.69139

2.67282

2.07677

1.31336

2.35808

2.35024

1.66594

1.10711

2.04498

2.04149

1.43146

T=1/2

5He

T=3/2

1/2+

5/2+

3/2+

1/2+

3/2+

5/2+

J=1/2+

J=3/2+

J=5/2+

R (fm)

E(R) (MeV)

11.064611.064611.110711.5842

6.419556.438676.537026.859

2.408392.417442.635032.83803

1.163831.190741.502591.6761

1.463271.545141.897922.02675

1.524931.645041.935952.03986

1.313361.424761.601411.73567

1.107111.189331.286131.4317

2

8

4

12

5H, J=1/2+

Kmax=12

Kmax=8

Kmax=4

Kmax=2

R (fm)

E(R) (MeV)

ER

-G

N

ER, G (MeV)

H5_hydra

0.0211.12Energie,largeur=4.27E+001.91E+00

1.9921.12Energie,largeur=2.18E+008.61E-01

-6.431.12Energie,largeur=2.04E+00-7.27E-01









-8.831.12Energie,largeur=2.05E+00-7.95E-01









-11.51.12Energie,largeur=2.07E+00-1.02E+00








1.91.12Energie,largeur=2.21E+007.02E-01

-4.261.12Energie,largeur=2.21E+004.20E-01


















0000000000

0000000000

0000000000

0000000000

0000000000

0000000000

0000000000

0000000000

0000000000

00

00

1.51.534.567.5910.512

Energies 1 :-3.31-5.999-7.916-8.41-7.47-5.772-3.882-2.121/2+

Energies 2 :-3.31-5.998-7.915-8.409-7.468-5.77-3.88-2.116

Energies 3 :19.09913.4698.5636.9127.0687.0016.6616.337

Energies 1 :-9.185-10.247-9.214-6.837-4.204-1.770.1641.5841/2-

Energies 2 :-9.184-10.247-9.213-6.836-4.202-1.7660.1691.593

Energies 3 :36.9127.74318.28912.2899.5258.2177.4426.922

Energies 1 :9.9014-1.007-3.131-2.962-1.695-0.2131.0923/2+

Energies 2 :9.9014-1.007-3.13-2.96-1.692-0.2091.098

Energies 3 :21.48715.72310.7248.7748.4078.037.5687.159

Energies 1 :-13.483-12.289-9.728-6.925-4.228-1.780.1581.5813/2-

Energies 2 :-13.482-12.288-9.727-6.923-4.226-1.7770.1641.59

Energies 3 :36.27627.48818.21912.2669.5178.2147.4416.922

1.51.534.567.5910.512

Energies 1 :-4.004-6.403-8.068-8.442-7.478-5.777-3.887-2.1241/2+

Energies 2 :-4.003-6.402-8.068-8.441-7.477-5.776-3.884-2.12

Energies 3 :16.74711.9747.8896.676.9816.9676.6446.326

Energies 1 :-10.43-10.981-9.474-6.897-4.222-1.7780.1591.5821/2-

Energies 2 :-10.429-10.98-9.473-6.896-4.219-1.7740.1651.591

Energies 3 :34.61126.25717.60412.0359.4238.1677.4146.904

Energies 1 :8.0363.262-1.244-3.179-2.973-1.699-0.2151.0913/2+

Energies 2 :8.0373.262-1.243-3.178-2.971-1.696-0.2111.097

Energies 3 :19.1414.22210.0288.518.3047.9867.5487.148

Energies 1 :-14.765-13.035-9.989-6.985-4.245-1.7880.1541.5793/2-

Energies 2 :-14.765-13.034-9.988-6.983-4.243-1.7840.161.588

Energies 3 :33.9452617.53612.0129.4158.1647.4136.904

1.51.534.567.5910.512

Energies-5.435-10.429-12.024-11.488-10.341-9.15-7.946-6.739

Energies-5.435-10.429-12.023-11.487-10.34-9.149-7.945-6.738

Energies16.27611.5677.4656.1556.4156.4486.2175.997

Energies-14.066-15.372-13.251-10.983-9.608-8.433-7.255-6.086

Energies-14.065-15.371-13.25-10.983-9.607-8.432-7.254-6.084

Energies33.35825.18116.40810.6928.0327.0046.5736.323

Energies2.071-3.359-6.704-7.977-7.785-6.918-5.875-4.828

Energies2.072-3.359-6.703-7.977-7.784-6.917-5.874-4.827

Energies18.87213.7819.5858.0447.867.6237.2696.94

Energies-16.747-16.614-13.511-11.009-9.612-8.434-7.256-6.086

Energies-16.747-16.614-13.51-11.008-9.611-8.433-7.255-6.085

Energies31.84924.04316.0210.5958.0026.9936.5696.322

-4.537

H5,1/2+H5,3/2+

1.515.614418.0699

310.9671313.1861

4.56.945399.06405

65.700837.58227

7.56.000277.43787

96.061937.22839

10.55.850366.89508

125.644116.58198

000000000000

000000000000

000000000000

000000000000

000000000000

000000000000

000000000000

000000000000

0.0150.020.0150.02

11.12Energie,largeur=4.45E+001.73E+0011.12Energie,largeur=3.52E+002.21E+001Energie,largeur=4.03E+002.00E+001Energie,largeur=3.33E+002.25E+00

21.12Energie,largeur=2.21E+007.08E-0121.12Energie,largeur=2.08E+001.19E+002Energie,largeur=2.18E+007.66E-012Energie,largeur=2.06E+001.36E+00

31.12Energie,largeur=2.21E+004.41E-0131.12Energie,largeur=2.47E+00-1.73E+003Energie,largeur=1.35E+00-3.05E+003Energie,largeur=2.04E+00-6.23E-01

41.12Energie,largeur=2.04E+00-5.80E-0141.12Energie,largeur=2.34E+00-1.36E+004Energie,largeur=2.07E+00-7.32E-014Energie,largeur=3.35E+002.10E-01

51.12Energie,largeur=2.31E+00-2.00E-0151.12Energie,largeur=3.35E+002.74E-015Energie,largeur=2.66E+005.31E-025Energie,largeur=3.37E+001.98E-01

61.12Energie,largeur=3.98E+001.80E+0061.12Energie,largeur=2.29E+00-1.22E+006Energie,largeur=2.35E+004.31E-026Energie,largeur=2.04E+00-4.82E-01

71.12Energie,largeur=3.58E+001.11E+0071.12Energie,largeur=2.27E+00-1.13E+007Energie,largeur=2.37E+003.90E-027Energie,largeur=2.11E+00-2.18E-01

81.12Energie,largeur=3.78E+001.38E+0081.12Energie,largeur=2.55E+00-1.94E+008Energie,largeur=2.57E+003.35E-028Energie,largeur=2.37E+00-1.83E+00

91.12Energie,largeur=2.16E+00-2.85E-0191.12Energie,largeur=2.55E+00-1.93E+009Energie,largeur=3.22E+00-3.86E-019Energie,largeur=2.32E+00-4.76E-01

101.12Energie,largeur=2.25E+00-2.37E-01101.12Energie,largeur=2.81E+00-2.60E+0010Energie,largeur=2.36E+00-8.02E-0210Energie,largeur=2.27E+00-5.34E-01

111.12Energie,largeur=2.23E+00-2.46E-01111.12Energie,largeur=2.54E+00-1.92E+0011Energie,largeur=2.99E+00-2.18E+0011Energie,largeur=2.30E+00-1.73E+00

0.02121.12Energie,largeur=2.58E+00-2.00E+0012Energie,largeur=3.77E+00-3.32E-0112Energie,largeur=2.29E+00-1.72E+00

11.12Energie,largeur=4.27E+001.91E+000.0250.0213Energie,largeur=3.08E+003.96E-02

21.12Energie,largeur=2.18E+008.64E-01Parameter=1.12Energie,largeur=3.29E+002.26E+001Energie,largeur=3.78E+002.13E+000.025

31.12Energie,largeur=2.03E+00-6.86E-01Parameter=1.12Energie,largeur=2.07E+001.52E+002Energie,largeur=2.11E+001.05E+001Energie,largeur=3.09E+002.28E+00

41.12Energie,largeur=2.03E+00-6.86E-01Parameter=1.12Energie,largeur=2.12E+00-9.83E-013Energie,largeur=2.15E+00-1.19E+002Energie,largeur=2.09E+001.68E+00

51.12Energie,largeur=3.04E+001.65E-01Parameter=1.12Energie,largeur=3.07E+002.06E-014Energie,largeur=2.15E+00-1.09E+003Energie,largeur=2.21E+00-1.16E+00

61.12Energie,largeur=2.04E+00-6.61E-01Parameter=1.12Energie,largeur=2.10E+00-7.99E-015Energie,largeur=3.20E+002.33E-014Energie,largeur=2.19E+00-1.09E+00

71.12Energie,largeur=2.04E+00-6.60E-01Parameter=1.12Energie,largeur=2.10E+00-7.87E-016Energie,largeur=2.15E+00-9.92E-015Energie,largeur=2.08E+00-6.75E-01

81.12Energie,largeur=1.96E+00-7.86E-01Parameter=1.12Energie,largeur=2.54E+00-2.00E+007Energie,largeur=2.15E+00-9.54E-016Energie,largeur=3.48E+00-2.45E+00

91.12Energie,largeur=2.31E+00-5.64E-01Parameter=1.12Energie,largeur=2.33E+00-1.24E+008Energie,largeur=2.13E+00-1.47E+007Energie,largeur=2.86E+00-2.12E+00



0.025Parameter=1.12Energie,largeur=3.99E+00-2.37E+0011Energie,largeur=2.17E+00-1.33E+0010Energie,largeur=2.33E+00-1.63E+00

11.12Energie,largeur=4.10E+002.04E+00Parameter=1.12Energie,largeur=3.33E+00-2.23E+0012Energie,largeur=2.50E+00-1.10E+0011Energie,largeur=3.63E+00-2.45E+00

21.12Energie,largeur=2.14E+001.09E+00Parameter=1.12Energie,largeur=3.08E+00-1.78E+000.02512Energie,largeur=3.35E+00-1.42E+00

31.12Energie,largeur=2.04E+00-7.74E-010.031Energie,largeur=3.56E+002.22E+000.03

41.12Energie,largeur=2.19E+00-4.75E-01Parameter=1.12Energie,largeur=3.10E+002.29E+002Energie,largeur=2.08E+001.33E+001Energie,largeur=2.91E+002.28E+00

51.12Energie,largeur=2.06E+00-6.90E-01Parameter=1.12Energie,largeur=2.13E+001.79E+003Energie,largeur=2.22E+00-1.18E+002Energie,largeur=2.18E+001.93E+00


71.12Energie,largeur=1.99E+00-1.58E+00Parameter=1.12Energie,largeur=1.86E+003.76E-015Energie,largeur=2.22E+00-1.10E+004Energie,largeur=1.76E+005.28E-01

81.12Energie,largeur=2.21E+00-7.90E-01Parameter=1.12Energie,largeur=6.63E+00-1.92E-016Energie,largeur=2.22E+00-1.09E+005Energie,largeur=6.10E+007.85E-01

91.12Energie,largeur=1.97E+00-1.33E+00Parameter=1.12Energie,largeur=2.61E+00-2.02E+007Energie,largeur=2.45E+00-1.93E+006Energie,largeur=2.76E+00-2.10E+00



0.03Parameter=1.12Energie,largeur=4.06E+00-2.32E+0010Energie,largeur=2.36E+00-1.72E+009Energie,largeur=4.33E+00-2.08E+00




41.12Energie,largeur=2.07E+00-9.57E-01Parameter=1.12Energie,largeur=4.13E+00-2.03E+000.0313Energie,largeur=4.26E+00-1.94E+00

51.12Energie,largeur=2.07E+00-8.93E-011Energie,largeur=3.37E+002.27E+00

61.12Energie,largeur=2.21E+00-1.93E+002Energie,largeur=2.10E+001.61E+00

71.12Energie,largeur=2.20E+00-1.92E+003Energie,largeur=2.21E+00-1.23E+00

81.12Energie,largeur=2.19E+00-1.86E+004Energie,largeur=1.95E+002.41E-01




8Energie,largeur=2.24E+00-1.72E+00

9Energie,largeur=1.95E+00-5.91E-01





0.02












0.025












0.03











111.12Energie,largeu

evidences for clustering

Documents