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 Presentation


  • 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



  • 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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