106
Y. Alhassid
10
2
10
4
10
6
0
5 10 15 20
10
0
10
2
10
4
10
6
5 10 15 20
E x (MeV)
5 10 15 20
59 Ni
61 Ni
63 Ni
60 Ni
ρ
~
(MeV
_
1
)
62 Ni
64 Ni
Fig. 2 Level densities of 59−64 Ni isotopes versus excitation energy E x . The AFMC level densities
(blue circles) are compared with level densities determined by proton evaporation experiments
(green symbols) [45], neutron resonance data when available (red triangles), and level counting
data at low excitation energies (blue histograms). Taken from Ref. [43]
of β and Eq. (5) is integrated to find the partition function Z(β). The entropy and
heat capacity are calculated from Eqs. (4), and the average state density is then given
by Eq. (3).
7.2.1 Mid-mass Nuclei
AFMC methods were applied to mid-mass nuclei using the complete fpg 9/2
shell [36, 39–41]. The single-particle levels and orbitals are taken from a Woods–
Saxon potential with spin–orbit interaction. The two-body interaction includes the
dominating components [42] of effective nuclear interactions: monopole pairing
and multipole–multipole interactions with quadrupole, octupole, and hexadecapole
components.
AFMC level densities of nickel isotopes 59−64 Ni are shown by the blue circles in
Fig. 2 [43]. These densities do not include the magnetic degeneracy 2J + 1 of each
level with spin J and are obtained by projection on M = 0 for even-mass nuclei and
M = 1/2 for odd-mass nuclei [44]. The AFMC densities are in excellent agreement
with experimental data without any adjustable parameters.
7.2.2 Heavy Nuclei: The Lanthanides
The AFMC approach was extended to the proton–neutron formalism, in which
protons and neutrons can occupy different shells [46]. This formulation was used
Y. Alhassid
10
2
10
4
10
6
0
5 10 15 20
10
0
10
2
10
4
10
6
5 10 15 20
E x (MeV)
5 10 15 20
59 Ni
61 Ni
63 Ni
60 Ni
ρ
~
(MeV
_
1
)
62 Ni
64 Ni
Fig. 2 Level densities of 59−64 Ni isotopes versus excitation energy E x . The AFMC level densities
(blue circles) are compared with level densities determined by proton evaporation experiments
(green symbols) [45], neutron resonance data when available (red triangles), and level counting
data at low excitation energies (blue histograms). Taken from Ref. [43]
of β and Eq. (5) is integrated to find the partition function Z(β). The entropy and
heat capacity are calculated from Eqs. (4), and the average state density is then given
by Eq. (3).
7.2.1 Mid-mass Nuclei
AFMC methods were applied to mid-mass nuclei using the complete fpg 9/2
shell [36, 39–41]. The single-particle levels and orbitals are taken from a Woods–
Saxon potential with spin–orbit interaction. The two-body interaction includes the
dominating components [42] of effective nuclear interactions: monopole pairing
and multipole–multipole interactions with quadrupole, octupole, and hexadecapole
components.
AFMC level densities of nickel isotopes 59−64 Ni are shown by the blue circles in
Fig. 2 [43]. These densities do not include the magnetic degeneracy 2J + 1 of each
level with spin J and are obtained by projection on M = 0 for even-mass nuclei and
M = 1/2 for odd-mass nuclei [44]. The AFMC densities are in excellent agreement
with experimental data without any adjustable parameters.
7.2.2 Heavy Nuclei: The Lanthanides
The AFMC approach was extended to the proton–neutron formalism, in which
protons and neutrons can occupy different shells [46]. This formulation was used