On the T>
giant dipole resonance in 48Ca and 90Zr.
I.V. Safonov[1],
M.H.Urin1, M.E. Stepanov[2], and
V.V. Varlamov[3]
The
photoabsorbtion cross section corresponding to excitation of the T>-component
of the giant dipole resonance (GDR) in medium mass nuclei 48Ca and 90Zr
having a relatively large neutron excess (T>=T+1, T=T<=(N-Z)/2
is the ground-state isospin) is described within a semimicroscopical approach.
The approach is based on the use of the continuum-RPA, phenomenological
isoscalar part of the nuclear mean field, momentum-independent Landau-Migdal
particle-hole interaction together with some partial self-consistency
conditions. This approach has been previously used for description of isobaric
analog resonances [1] and T<-GDR [2].
The
experimental data concerned with parameters of the T>-GDR for 48Ca were found from Ref. [3] and for 90Zr
were deduced using the method of Ref. [4] of joint analysis of GDR proton and
neutron decay channels. This analysis is based on the data from Ref. [5] and
Ref. [6] correspondingly.
Supposing
that isospin is a good quantum number, one can express the photoabsorption
cross section s>(w) (w is the
gamma-quantum energy) via the charge-excange (in the b(+)
channel) dipole strength function S(+)(w(+)) taken at the
energy w(+)=w-D (see, e.g., Ref.
[7]). Here, D is the Coulomb
displacement energy identified with the mean Coulomb field averaged over the
neutron excess density. Using the same model parameters as in Ref. [1] we
calculate the charge-exchange dipole strength functions S(±)(w(±)) for 48Ca
and 90Zr parent nuclei (w(-) is the
excitation energy in the b(-)
channel). It was found that the non-energy-wieghted sum rule 
(n(-)(r) is the
neutron excess density) is reproduced in our calculations with an accuracy as
well as 1%. Using the calculated cross section s>(w) we evaluate the mean excitation energy 
of the T>-GDR and also
RMS energy dispersion 
. A
rather small spreading width of parent T>-states (1.0 ¸ 1.5 MeV) allows us to identify
approximately the calculated RMS width G>=2.35D> with the total
width of the T>-GDR. The calculated quantities are found
to be in a reasonable agreement with the available experimental data (see the
Table 1). It is worth to note, however, that after taking momentum–dependent
forces into account the calculated energies w> are
expected to be increased. The respective calculations are planned to be done
within the same model, which has been reasonably used for description of T<-GDR
in Ref. [2].
This work
is partially supported by the RFBR (grant ¹ 02-02-16655) and by the Programme
«Universities of Russia» (grant ¹ ÓÐ.02.01.025).
Table 1.
Parameters of the T>-GDR in 48Ca and 90Zr.
|
Nucleus |
w> , MeV |
w>exp, MeV |
G, MeV |
Gexp, MeV |
|
48Ca |
22.05 |
25.80 |
6.91 |
6.23 |
|
90Zr |
18.48 |
20.79 |
4.86 |
4.10 |
[1] M.L.Gorelik
and M.H.Urin, Phys. Rev. C63, 064312 (2001); Yad. Fiz. 64, ¹3, 560 (2001).
[2] V.A.Rodin and
M.G.Urin, Phys. Rev. C66, 064608 (2002).
[3] G.J.O’Keefe, M.N.Thompson,
Y.I.Assafiri, R.E.Pywell, and K.Shoda, Nucl.Phys., A499, 239 (1987).
[4] V.V.Varlamov and M.E.Stepanov, Yad.
Fiz. 65, 1 (2002).
[5] K.Shoda, M.Sugawara, T.Saito, and H.Miase,
Nucl.Phys., A221, 125 (1974).
[6] A.Lepretre, H.Beil, R.Bergere, P.Carlos, A.Veyssiere, and
M.Sugawara, Nucl.Phys., A175 (1971) 609.
[7] M.G.Urin,
"Relaxation of nuclear excitations" (in Russian), Energoatomizdat,
Moscow, 1991.