Problem of Level Densities
141
the excitation of levels with spin J = J 0 ± 1/2. To obtain the total level density,
one must correct the inferred level density for levels of other J values. It is usually
assumed that the spin distribution proposed by Bethe is valid, in which a correction
factor would be
ρ T (E) =
ρ(E, 1/2)
S(1/2)
J
S(J )
(7)
for even-A targets or
ρ T (E) =
ρ(E, J 0 − 1/2) + ρ(E, J 0 + 1/2)
S(J 0 − 1/2) + S(J 0 + 1/2)
J
S(J )
(8)
for non-zero spin targets. An additional factor of two is applied to the right hand side
of Eqs. 7 and 8 to correct for levels of the other parity. It is obvious from Ref. [4]
that the correction formula will be different for deformed nuclei. The corresponding
formulas based on Eq. 6 will be
ρ T (E) =
ρ(E, 1/2)
J S(J )R 1 (E, J )
S(1/2)R 1 (E, 1/2)
(9)
and
ρ T (E) =
ρ(E, J 0 − 1/2) + ρ(E, J 0 + 1/2)
S(J 0 − 1/2)R 1 (E, J 0 − 1/2) + S(J 0 + 1/2)R 1 (E, J 0 + 1/2)
×
J
S(J )R 1 (E, J )
(10)
for J 0 = 0 and J 0 = 0, respectively. In each case, the right hand side also must be
multiplied by a factor of two to correct for levels of the missing parity.
Two compilations of level density parameters from low-energy resonances have
been published in Refs. [5, 6]. In the compilation by Rohr [5], there is a specific
statement that the results did not show an enhanced level density for deformed
nuclei. The conclusion of Ref.[6] is more confusing. The authors derived level
density parameters using the conventional Bethe formulas. They find that the a
values for deformed nuclei are close to those for nearby spherical nuclei. They then
divide the level density by the factor predicted in Ref. [2, 3]. They then calculated
the revised a which they refer to as intrinsic. Despite this second step, it is still true
that the authors of Ref. [6] do not find higher level densities for deformed nuclei.
An important point is that both Refs. [5, 6] used the Bethe spin distribution for
both deformed and spherical nuclei. Bethe [1] specifically states that he assumes
spherical symmetry in deriving his spin formula.
In table 1 the results of Iljinov et al. [6] are summarized for some deformed
nuclei. For each of the nuclei listed, the neutron binding energy, the observed spins,
141
the excitation of levels with spin J = J 0 ± 1/2. To obtain the total level density,
one must correct the inferred level density for levels of other J values. It is usually
assumed that the spin distribution proposed by Bethe is valid, in which a correction
factor would be
ρ T (E) =
ρ(E, 1/2)
S(1/2)
J
S(J )
(7)
for even-A targets or
ρ T (E) =
ρ(E, J 0 − 1/2) + ρ(E, J 0 + 1/2)
S(J 0 − 1/2) + S(J 0 + 1/2)
J
S(J )
(8)
for non-zero spin targets. An additional factor of two is applied to the right hand side
of Eqs. 7 and 8 to correct for levels of the other parity. It is obvious from Ref. [4]
that the correction formula will be different for deformed nuclei. The corresponding
formulas based on Eq. 6 will be
ρ T (E) =
ρ(E, 1/2)
J S(J )R 1 (E, J )
S(1/2)R 1 (E, 1/2)
(9)
and
ρ T (E) =
ρ(E, J 0 − 1/2) + ρ(E, J 0 + 1/2)
S(J 0 − 1/2)R 1 (E, J 0 − 1/2) + S(J 0 + 1/2)R 1 (E, J 0 + 1/2)
×
J
S(J )R 1 (E, J )
(10)
for J 0 = 0 and J 0 = 0, respectively. In each case, the right hand side also must be
multiplied by a factor of two to correct for levels of the missing parity.
Two compilations of level density parameters from low-energy resonances have
been published in Refs. [5, 6]. In the compilation by Rohr [5], there is a specific
statement that the results did not show an enhanced level density for deformed
nuclei. The conclusion of Ref.[6] is more confusing. The authors derived level
density parameters using the conventional Bethe formulas. They find that the a
values for deformed nuclei are close to those for nearby spherical nuclei. They then
divide the level density by the factor predicted in Ref. [2, 3]. They then calculated
the revised a which they refer to as intrinsic. Despite this second step, it is still true
that the authors of Ref. [6] do not find higher level densities for deformed nuclei.
An important point is that both Refs. [5, 6] used the Bethe spin distribution for
both deformed and spherical nuclei. Bethe [1] specifically states that he assumes
spherical symmetry in deriving his spin formula.
In table 1 the results of Iljinov et al. [6] are summarized for some deformed
nuclei. For each of the nuclei listed, the neutron binding energy, the observed spins,