THE BIG DIPexperimental and systematic

discussions of neutron binding in very neutron-rich nuclides

William B. Walters

Department of Chemistry

University of Maryland

• First, let me thank the JINA group for the kind invitation to talk about neutron-rich nuclides here in Michigan at Gull Lake.

• It is a real privilege to speak to an audience that includes people who can and and probably will be able to test some of these ideas in future experiments.

I am just back at Maryland after a 6-month Sabbatical visit in Mainz that was made possible by a Research Award from the Alexander von Humboldt Stiftung . First, I wish to thank Professor Karl-Ludwig Kratz, for his efforts with AvH and Mainz that made the visit in Mainz possible, and both he and Gisela for making the visit interesting and enjoyable

And, also the U. S. Department of Energy who has provided strong support for the Maryland part of this work.

I also must acknowledge the hard work, long discussions, and continuous efforts of BERND PFEIFFER, PETER MÖLLER, DAREK SEWERYNIAK, and ANDREAS WÖHR and a large group of Mainz, Maryland, ISOLDE and Argonne students and post docs, along with many detailed theoretical discussions with both JIRINA RIKOVSKA from Oxford/Maryland and ALEX BROWN from Michigan State.

Reviews of Modern Physics, 29, 47 (1957).

Since BBFH showed in the Figure at the left the connection between elemental abundances the location of closed neutron shells, study and knowledge of the structure and decay of those nuclides involved in nucleosynthesis has been entwined with astrophysical considerations about how, when, and where nucleosynthesis takes place.

Cd48 76

124

4+

6+

613

0

1385

2140

Cd48 78

126

0+

2+

4+

0

Cd48 80

128

0+ 0

652

2+ 14281467

652

814

5± 1847 5± 1869

2+ 645645

4+ 1429784

401

0+

2+

Cd48 82

130

0+ 0

Evidence for shell quenching

0

500

1000

1500

2000

0

0.5

1

1.5

2

2.5

3

45 50 55 60 65 70 75 80 85

CdPd

Te

Cd

Te

Pd

4+/2+ ratio

+2 energies (keV)

calculated

calculated

Pd calculations:Kim, Gelberg,Mizusaki, Otsuka, von Brentano,NP A 604,163 (1996).

T. Kautzsch, et al., E. P. J. A 9, 201 (2000).

963

0

798

0

645

0

491

d5/2

370

332

0

160

0

270

0

527

0

724

0

815

0

851

00000

832769

g7/2

0 0

1806

0

g7/2d5/2d5/2 g7/2d5/2A = 101 103 105 107 109 111 113 115 117 119 121 123 125 127 129 131 133 135 207

N = 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 126

Monopole shift in odd-mass Sb nuclides.

282

J. Shergur et al., PRC 65, 034313 (2002)

Decay of Sn-135 to levels of Sb-135 RILIS (CERN/ISOLDE)

K.-L. Kratz, B. Pfeiffer et.al

Today, I come from the Kratz,Thielemann, Möller, etc.,school of nuclear astrophysics.

The basic assumptions about the r-process that underlie the discussion are that r-process must take place in a neutron-rich environment where:

neutron densities must range up to 1027 to produce elements beyond lead,

that at some point neutron densities are encountered at the level of 1020-23 to make the peak at A = 130 (at 1027, little would be left at A = 130),

the temperature is over 109 K with an appropriate gamma ray flux,

during the process equilibrium exists between (,n) and (n, ) reactions,

that the process ends very quickly…termed “freeze-out” and the nuclides left at the end undergo beta decay (with beta-delayed neutron emission) toward the line of stability. In particular, this process produces the “r-only” nuclides like 110Pd, 124Sn, and 130Te.

that the yields shown in the abundance curve arise from material that is “waiting” to move on at “freeze-out” and subsequently decays back to stable nuclides with higher Z,

that the peaks in the abundance curves arise from material that has accumulated at a “waiting-point” whose forward movement is “slowed down”,

that valleys in the abundance curves arise from material where forward movement is quite rapid and, hence, there is little accumulated material to decay toward stability.

Now, I want to describe some details about the (,n) = (n, ) equilibrium that show where and how nuclear structure and decay properties on nuclei play a role in r-process movement.

(,n)(n, )

decay

Sn = 5.0 2.3 4.5 2.1 4.3 1.9 4.1 1.3 3.4 0.9 2.5

36Kr 98 99 100 101 102 103 104 105 106 107 108N = 62 63 64 65 66 67 68 69 70 71 72

Sn = 2.5 for 104Rb67…the process moves on.

Waiting points always have even neutron numbers.If the neutron density is larger, the waiting point could move to 106.If the temperature is higher, the waiting point could move to 102.

Kr half-lives 104(46) 48 23 15 9 5 ms.

The decay and waiting responsible for the formation of the A = 130 peak is illustrated. What are shown are the half-lives and Sn values for the N = 82 And N = 83 isotones. As you can see, the neutron is unbound in 123Zr, whereas the neutron is rather tightly bound for all of the N = 82 isotones.

You can also see that below Z = 44, the half-lives are so short that there is very little waiting.

With these half-lives, “waiting starts atZ = 44, Ru, and increases toward the major blockade in this mass region,130Cd.

Finally, at 132In, the Sn is sufficiently high to permit neutron capture to proceed on to the next waiting point, 135In

Half life (ms)

Half life (ms)Neutron separationEnergy (MeV) Sn

Conclusion: The critical values from nuclear structure and decay measurements that are needed are half-lives and neutron separation energies (masses).

P. Möller, J. R. Nix, and K.-L. Kratz, ADNDT 66, 131(1997).

Sn (MeV)

Sn (MeV)

Sn (MeV)

Sn (MeV)

Sn (MeV)

Sn (MeV)

Sn (MeV)

Sn (MeV)

Sn (MeV)

Znuclides N = 82 N = 83

49 In=131 132 227 2016.2 2.7

48 Cd 130 131 165 686.2 2.0

47 Ag 129 130 46 425.6 2.0

46 Pd 128 129 56 1175.5 1.5

45 Rh 127 128 22 185 1.2

44 Ru 126 127 34 364.9 0.7

43 Tc 125 126 9 84.3 0.7

42 Mo 124 125 11 94.2 0.1

41 Nb 123 124 3.5 4.13.4 0.08

40 Zr 122 123 4.3 3.83.6 -0.6

-2

0

2

4

6

8

10

12

50 55 60 65 70 75 80 85

Neutron Separation Energies

ZrKrRuSn

Sep

arat

ion

Ene

rgy

in M

eV

Neutron Number

From Möller, Nix and Kratz, ANDT 66, 131 (1997).

In particular, it is the flattening of the separation energies for theZr (and adjacent) nuclides that results in the large dip in yields for the A = 120 region.

Observe that there is NO leveling for theSn nuclides!!!!

The Sn points areExperimental.

d 5/2 7/2g

Sn

In

Cd

Ag

Pd

Rh

Ru

Tc

Mo

Nb

Zr

Y

Sr

Rb

Kr

Br

Se

As

Ge

Ga

Zn

Cu

Ni

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

f

p

p

s1/2

5/2

h11/2

1/2

3/2

3/2d

g

N

Z

Heaviest known yrast structures Heaviest known half lives

160 ms 46 ms56 ms22 ms

9/2

34 ms 9 ms11ms 3 ms 4 ms

11/2- 21703/2+ 2042

1/2+ 1205

131 Sn50 81

7/2+ 2201

7/2+ 2434

91 Zr40 51

5/2+ 0 5/2+ 1654

1/2+ 331

11/2- 50(75)3/2+ 0

Neutron monopole shifts from Zr-90 to Sn-132

3/2+ 11037/2+ 1264

5/2+ 1400

11/2- 2268

97 Zr40 57

1/2+ 0

121 Zr40 81

5/2+ 3000

11/2- 0

3/2+ 1200

7/2+ 2000

1/2+ 1800

extrapolatedAdding six moreN = 4 shell d-5/2 neutrons beyond the ten g-9/2 neutrons leads to a neutron skin that inhibits the binding of the N = 5 oscillator shell h-11/2 neutrons by theN = 3 shell protons.

11/2- -1003/2+ 0

1/2+ -1340

7/2+ +110

91Zr40 51

5/2+ -2760

Neutron monopole shifts from Zr-90 to Gd-145

Neutron levels normalized to the d-3/2 particle.

N = 81 hole nomalized to thed-3/2 hole in Sn-131.11/2- +900

3/2+ 0

1/2+ -1600

7/2+ -70

97Zr40 57

5/2+ -3080

11/2- -50(75)

3/2+ 0

1/2+ -331

7/2+ -2434131Sn50 81

5/2+ -1654

extrapolated

11/2- +1000

3/2+ 0

1/2+ -6507/2+ -500

121Zr40 81

5/2+ -2000

11/2- -334

3/2+ 0

1/2+ -308

133 Te52 81

11/2- -526

3/2+ 0

1/2+ -288

135Xe

54 81

11/2- -661

3/2+ 0

1/2+ -283

Ba56 81

137

11/2- -754

3/2+ 0

1/2+ -255

Ce58 81

139

11/2- -757

3/2+ 0

1/2+ -194

Nd60 81

141

11/2- -754

3/2+ 0

1/2+ -110

Sm62 81

143

11/2- -722

3/2+ 0

1/2+ +27

Gd64 81

Continued addition of g7/2 protons Beyond Z = 50 continues to result in stronger binding for the h11/2

neutron up through Z = 58

145

pf proton core

pf neutron core

10 g9/2 neutrons

6 d5/2 neutrons

8 g7/2 neutrons

12 h11/2 neutrons

little neutron skin

BIG neutron skin

Adding 10 g9/2 protons

Adding 8 g7/2 protons

In other words, it takes ALL 18 g9/2 protons to fully bind the 12 h11/2 neutrons.

Binding of various layers of neutrons by pf shell protons.

40 Zr 4080

40 Zr 5090

40 Zr 5696

40 Zr 70110

40 Zr 82122

50 Sn 82132

58 Ce 82140

11/2- -50(75)

3/2+ 0

1/2+ -331

7/2+ -2434

131Sn50 81

5/2+ -1654

N = 81 hole nomalized to thed-3/2 hole in Sn-131.

11/2- -334

3/2+ 0

1/2+ -308

133 Te52 81

11/2- -526

3/2+ 0

1/2+ -288

135Xe

54 81

11/2- -661

3/2+ 0

1/2+ -283

Ba56 81

137

11/2- -754

3/2+ 0

1/2+ -255

Ce58 81

139

11/2- -757

3/2+ 0

1/2+ -194

Nd60 81

141

11/2- -754

3/2+ 0

1/2+ -110

Sm62 81

143

11/2- -722

3/2+ 0

1/2+ +27

Gd64 81

145

11/2- -679

3/2+ 0

1/2+ +72

Dy66 81

147

11/2- -631

3/2+ 0

1/2+ +111

Er68 81

149

(749)(751)

(742)

In this region as Z increases from 50 to 58, the protons are filling the g7/2 orbitals, and then from 58 to 64 the protons are filling the d5/2 orbitals.

Starting at Z = 65, the protons are fillingthe s1/2, d3/2, h11/2 orbitals.

The h-11/2 neutrons seem insensitive to h-11/2 protons!!

133Sn

7/2- 0

3/2-854

9/2-

1561

1/2-1656

5/2-

2004

134Te

0+

2+1280

135

3/2-

658

137

3/2-

601

9/2-1220

1/2-

5/2-

986

Te136

Xe

2+1313

Xe139

3/2-

627

9/2-1283

1/2-

5/2-

1082

138

2+

Ba Ba

13/2+16199/2-

141

3/2-

662

9/2-13551/2-

5/2-

1137

140

2+

Ce

1596

13/2+

19159/2-

Ce143

3/2-

742

9/2-14071/2-

5/2-

1306

142

2+

Nd

1575

13/2+

17399/2-

Nd145

3/2-

893

9/2-

1423

1/2-5/2-

144

2+

Sm

1660

13/2+

9/2-

Sm147

3/2-1152

9/2-

1397

1/2-

146

2+

Gd

1971

13/2+

9/2-

Gd 149

3/2-

9/2-

1/2-

148

2+

Dy

1677

13/2+

9/2-

Dy 151

3/2-

9/2-

801

1/2-

150

2+

Er

1578

13/2+

9/2-

153

9/2- 567

152

2+

Yb

1531

13/2+

9/2-

Er Yb154

2+

Hf

1513

N =83 ISOTONES

7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+ 7/2- 0+

1220

9/2-1246

1/2- 1083

1436

1035 984

5/2-1091

13/2+

2625

1423

13/2+

2713

1774

C2S =6

C2S =3

C2S =6

C2S =4

1846

g7/2 protons d5/2 protons h11/2 protons

νh9/2

Acta Physica Pol. B 27, 475 (1996).

Sn50 83

1337/2- 0

3/2- 854

νh9/2 15619/2-

νp3/2

νf7/2

1/2- 1656νp1/2

5/2- 2004νf5/2

13/2 + 2694(200)νi13/2

Sn = 2455 (45)

0νf7/2

normall2νf7/2

νf7/2

0.7 l2 0.4 l2

854νp3/2

νp3/2

νp3/2

1561νh9/2

νh9/2

νh9/2

1656νp1/2

νp1/2

νp1/2

2004νf5/2 νf5/2νf5/2

2694νi13/2

νi13/2 νi13/2

0

154

2561

946

1920

3800

0

-500

3600

250

1850

5000

Sn50 96146

Sn50 102

152

Pb82 125207

7/2- 0

3/2- 1442

νh9/2 -10739/2-

νp3/2

νf7/2

1/2- 2340νp1/2

5/2- 1770νf5/2

13/2 + 708νi13/2

3/2- 0

1/2- 2023

5/2- 3991

49

20 29Ca

9/2+ 6000

3/2- 0

1/2- 11125/2- 769

57

28 29Ni

9/2+ 3009

3/2- 1095

1/2- 588

5/2- 1451

89

40 49Zr

9/2+ 0

1/2- 0

3/2- -1140

5/2- -694

67

28 39Ni

9/2+ 10079/2+ - 5/2- gap ≥ 2 000 keV

9/2+ - 5/2- gap =1700 keV

9/2+ - 5/2- gap = ~2200 keV9/2+ - 5/2- gap = ~1500 keV

7/2- -75007/2- -65007/2- -55007/2- -2500

3/2- -100043

14 29Si

7/2- 0

1/2- 1000

5/2- 6000

New Shell Gapat N = 34???

Monopole shift of the p3/2 and p1/2 neutron orbitals with changing nuclear size and N/Z ratio.

ProjectedProjected

Possible double magic nuclide 48Si34

W. B. Walters, Seyssins, France, AIP Conference Series 447, 196 (1998).

Conclusion:

The “big dip” can be traced to what I believe is a calculated overbinding for the h-11/2 neutron orbitals between N = 70 and N =82. Data exist that can be interpreted to indicate that the binding of h-11/2 neutrons is quite sensitive to the number of g-7/2 ( and by inference, g-9/2 protons) in the nucleus, as well as the number of gdds neutrons present.

The challenge for experimental science is to determine as many properties of these very neutron-rich nuclides as possible, and the challenge for theorists is to improve the way that nuclear models describe very neutron-rich nuclides.

Stated another way…..RIA must be built with design goals that include the study of Zr-122 and neighboring nuclides.

Thank you for your attention.

Deformation changes all of that for Sr and Zr by bringing g9/2 protons up from below Z = 40

We start with spherical 98Sr60 where shape coexistence is well known and arises from the 10 neutrons and four protons into downsloping orbitals.

And you can see that the nucleus can take another pair of protons for Zr.

The important point is that these shifts move 4 to 6 protons from the pf orbitals into the g9/2 orbitals and permit much better binding of the h11/2 neutrons.

Adding 10 more neutrons up to N = 70 is seen to be rather neutral and perimts the g9/2 protons to stay up to that point.

However, beyond N = 70, additional neutrons drive the nucleus back toward sphericity and drive the protons back into the pf shell, thereby once again loosening the binding for the h11/2 neutrons.

Notice that there IS a valley at A = 180…the N = 126 shell works.

Sn

In

Cd

Ag

Pd

Rh

Ru

Tc

Mo

Nb

Zr

Y

Sr

Rb

Kr

Br

Se

As

Ge

Ga

Zn

Cu

Ni

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

ε ≈ 0.4

f

p

p

s1/2

5/2

9/2

h11/2

1/2

3/2

3/2dd5/2

A = 112 A = 124

N = 2 Z

g

N →

↑Ζ

r processpath

N = 1.6 Z

Heaviest known yrast structures