FermiGasy

W. Udo Schröder, 2004 FermiGas Model 2 Particles in Ideal 1D Box Approximate picture: independent particles in mean field produced by interactions of all nucleons  calculate single-particle spectrum  approximate potential (first neglect V Coulomb ) Average Potential V(x) a x  1 (x)  2 (x)  3 (x)  n / 1  1 (x),  2 (x),  3 (x)

W. Udo Schröder, 2004 FermiGas Model 3 Particles in Ideal Multi-D Box State Space n i = 1,2,3,.. i=x,y,z  2D x y a x =a y =a z =100 nxnx nyny nznz 

W. Udo Schröder, 2004 FermiGas Model 4 Density of Fermi Gas States nxnx nznz  3D box, side length a, volume V = a 3 Every point on 3D-integer grid in p-space represents one state n»1  continuous approximation How many states dn in {p, p+dp}  {, +d}? dn/d  = A nucleons FF empty

W. Udo Schröder, 2004 FermiGas Model 5 The Fermi Energy dn/d  = A nucleons FF empty  A = matter density Fermi energy  (nucleon density) 2/3  Fast nucleons in dense matter Fill all single-particle states with 4 nucleons each (spin, isospin up/down)  degenerate FG Nuclear matter:  F = 37 MeV  A = 0.16 fm -3 k F = 1.36 fm -1 p F =  k F =268MeV/c Mean field potential U 0 =  F + B/A = 45 MeV

W. Udo Schröder, 2004 FermiGas Model 6 Total Energy r 0 = ( ) fm Treat all nucleons same with 2 s x 2  qu. numbers, degenerate states

W. Udo Schröder, 2004 FermiGas Model 7 2-Component Fermi Gas FF VnVn VpVp r r Mix of 2 independent (n,p) gases Protons feel Coulomb potential V Coul In real nuclei  F (N)   F (Z) Otherwise conversion ( decay) n  p  Nuclei have N > Z pxpx pypy pF=kFpF=kF Ground state: degenerate FG (T=0) Excited state: non degenerate FG (T≠0) pxpx pypy T Ground State

W. Udo Schröder, 2004 FermiGas Model 8 r 0 = 1.4 fm

W. Udo Schröder, 2004 FermiGas Model 9 Asymmetry Energy This is the origin of the asymmetry energy in the LDM !

Seminar: Statistical Decay of Complex Systems (Nuclei) 1.Nuclear Models: The Fermi Gas 2.Density of states of A-body system Temperature concept and level density 3.Spin and structure dependence of level densities 4.Weisskopf model of statistical decay Examples and applications 5.Hauser-Feshbach model 6.Dynamical effects 7.Pre-equilibrium decay 8.Compound nucleus reactions 9.Multi-fragment decay