# nuclear level densities

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Edwards Accelerator Laboratory. Nuclear Level Densities. Steven M. Grimes. Ohio University Athens, Ohio. Fermi Gas Assumptions: 1.) Non-interacting fermions 2.) Equi-distant single particle spacing (U) ∝ exp [ 2√au ] / U 3/2 generally successful Most tests at U < 20 MeV - PowerPoint PPT PresentationTRANSCRIPT

Nuclear Level DensitiesEdwards Accelerator LaboratorySteven M. GrimesOhio UniversityAthens, Ohio

Nuclear Level DensitiesFermi Gas Assumptions:

1.) Non-interacting fermions

2.) Equi-distant single particle spacing(U) exp[2au] / U3/2generally successful

Most tests at U < 20 MeVFor nuclei near the bottom of the valley of stability

Nuclear Level DensitiesDATA:(1) Neutron resonances U 7 MeVnear valley of stability(2) Evaporation spectraU 3 15 MeVnear valley of stability(3) Ericson FluctuationsU 15 24 MeVnear valley of stability(4) Resolved LevelsU 4 5 MeVMost points for nuclei in bottom of valley of stability

Nuclear Level DensitiesStudy of Al-Quraishi, et al.20 A 110

Found a = A exp[-(Z-Z0)2] 0.11 0.04 Z -- Z of nucleus Z0 -- Z of stable nucleus of that Z

Reduction in a negligible if Z-Z0 1

Nuclear Level DensitiesStudy of Al-Quraishi, et al.

Significant effect for Z-Z0 = 2

Large effect for| Z-Z0 | 3

Nuclear Level DensitiesIsospin: (N-Z)/2 = TZT TZ

At higher energies, have T=2 multiplets 16C, 16N, 16O, 16F,16Ne(TZ=0) > (TZ=1) > (TZ=2)predicts a = A exp( (N-Z)2 ) 16N16O16FT = 0T = 1

Nuclear Level DensitiesCONCLUSION

Only one analysis finds a lower off of stability line

Limited data is the central problem

Nuclear Level DensitiesBulk of Level Density information comes from neutron resonances

Example: n + 32S 33S*

At low energy (neutrons) find1/2+ levels at about 7 MeV of excitation

Not feasible for unstable targets Only get density at one energy Need ( = Jz21/2 ) to get total level density

Nuclear Level DensitiesPREDICTIONS

A compound nucleus state must have a width which is narrow compared to single particle width

This indicates compound levels will not be present once occupancy of unbound single particle states is substantial.

Nuclear Level DensitiesAssume we can use Boltzmann distribution as approximation to Fermi-Dirac distribution

Since U = a2

= U/a istemperaturea is level density parameterU is excitation Energy

Nuclear Level DensitiesIf occupancy of state at excitation energy B is less than 0.1

exp[ -B/ ] = exp[ -Ba/U ] 0.1a A/8

exp[ -B A/8U ] 0.1so, -B A/8U -2.3UC ( AB2 / 42.3 )

Above this energy we will lose states

Nuclear Level DensitiesAB(MeV)U(MeV) 20 8 30.3200 8303. 20 6 17.04200 6170.0 20 4 7.58200 4 75.8 20 2 1.9 200 2 19

Nuclear Level DensitiesFor nucleosynthesis processes, we will frequently have B ~ 4 MeV for proton or neutron

For A ~ 20 level density is substantially reduced by 10 MeV if B = 4

For A ~ 20 level density limit is B if B = 2 MeV

Substantial reduction in compound resonances

Nuclear Level DensitiesWill also reduce level densityfor final nucleus in capture

We also must consider parity

In fp shell even-even nucleihave more levels of + parityat low U than - parity

Even-odd or odd-even havemostly negative parity states

Nuclear Level DensitiesThus, compound nucleus states not only have reduced (U) but also suppress s-wave absorption because of parity mismatch

Nuclear Level DensitiesAlso have angular momentum restrictions

Could have even-even targetnear drip-line where g9/2 orbit is filling

Need 1/2+ levels in compound nucleus

Nuclear Level DensitiesLow-lying states are 0+ g9/2 9/2+or2+ g9/2 5/2+, 7/2+, 9/2+, 11/2+, 13/2+

At low energy 1/2+ statesmay be missing

No s-wave compound nuclear(p,) (or (n,)) reactions

Nuclear Level DensitiesEXPERIMENTAL TESTSMeasure:55Mn(d,n)56Fe

58Fe(3He,p)60Co58Fe(3He,d)57Fe58Fe(3He,n)60Ni

58Ni(3He,p)60Cu58Ni(3He,)57Ni58Ni(3He,n)60Zn

Nuclear Level DensitiesResult: lower a higher average Elower multiplicity

If compound nucleus is proton richAl Quraishi term will furtherinhibit neutron decayChange in a a (a-a)Ep(Ep)

Nuclear Level Densities

Nuclear Level DensitiesSpan range of Z-Z0 valuesup to ~ 2.5

Find evidence that a /A decreaseswith Z-Z0 increasing

Nuclear Level DensitiesCurrently calculating these effects

Woods-Saxon basis

Find single particle state energies and widths

Compare with all sp states with including only bound or quasibound orbits

Nuclear Level DensitiesExpect reduction in a if Z-Z0 2, 3

As Z-Z0 increases, new form with peak at 5-10 MeV may emerge (i.e. (20) 0)

Nuclear Level DensitiesCalculations and measurements underway

1.) Hope to determine whether off of stability line a drops

2.) is form a = A exp[-(Z-Z0)2] appropriate?

3.) As drip line is approached, we may have to abandon Bethe form and switch to Gaussian

Nuclear Level DensitiesHEAVY ION REACTIONS

Can get to 30-40 MeV of excitation with lower pre-equilibrium component

Cannot use projectile with A about equal to target (quasi-fission)

Nuclear Level DensitiesHEAVY ION REACTIONS

Recent Argonne measurements60Ni + 92Mo60Ni + 100Mo

got only 30-35% compound nuclear reactions

Jcontact too high

Not enough compound levels

Nuclear Level DensitiesProjectiles with A < half of target A are better

Want compound nuclei with|Z-Z0| 2 to compare with |Z-Z0| 0

Nuclear Level DensitiesREACTIONS

24Mg + 58Fe 82Sr*24Mg + 58Ni 82Zr*18O + 64Ni 82Kr*

Excitation energy 60 MeV

82Kr has Z = Z082Sr has Z = Z0 + 282Zr has Z = Z0 + 4

Nuclear Level DensitiesCompare:

Rohra A

Al Quraishia A exp[ (Z-Z0)2 ]

Nuclear Level DensitiesDecay FractionsRohr.96 n.04 p.005 Al-Quraishi.93 n.06 p.01 82Kr.67 n.25 p.05 .02 d.61 n.33 p.05 .01 d82Sr

Nuclear Level DensitiesDecay FractionsRohr.43 n.49 p.06 .02 dAl-Quraishi.36 n.55 p.07 .02 d82Zr

Nuclear Level DensitiesRohr: Higher a for Z-Z0 2 Al-Quraishi: Lower a for Z-Z0 2 Get softer spectrum with Rohr

More 4-6 particle emissions thanAl-Quraishi

Nuclear Level DensitiesCalculations

Solve for single particle energies in a single particle (Woods-Saxon) potential

Compare level density including all single particle states with level density including only those with < 500 keV

Nuclear Level DensitiesCalculations

Small effects for Z Z0

Large effects for Z-Z0 4

Looking at including two body effects in these calculations with moment method expansions

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Nuclear Level DensitiesCONCLUSIONSAstrophysics has need forlevel densities off of thestability line for A 100

Data base in this region ( Z-Z0 2 ) is poor

Model predicts that a decreaseswith |Z-Z0|

Need more reaction data for nucleiin the region of |Z-Z0| 2

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