#### 1. Introduction

Charge-exchange states are associated with the charge excitation branch and correspond to excited states of isobar nuclei. They are manifested in the corresponding charge-exchange reactions such as (
*e*), (*p,n*), (*n,p*), (
*t*), (*t*,

The most complete experimental studies of the entire spectrum of the charge-exchange excitations for nine tin isotopes
*t*)Sb charge-exchange reaction at the energy *E*(
*E*

#### 2. Method of calculation

Charge-exchange excitations of nuclei are described in the microscopic theory of finite Fermi systems TFFS by the system of equations for the effective field [7]:

(1)
where

(2)
with the parameters

The energies of charge-exchange excitations were calculated both in the self-consistent TFFS and in its approximate model variant [5], which allowed obtaining analytical solutions for the most collective states. For energies *E*
*E*
*
* (

*k*= 0 for GTR and

*k*= 1, 2, 3 for PR1, PR2, and PR3) divided by the average energy

*E*l s
of spin–orbit splitting [8] at Δ

*E*

*E*l s
, has the form:

where *x =* Δ*E*/*E
*, Δ

*E*= (4/3)ε

*N-Z*)/

*A*MeV, ε

*a*

*a*

·

*p*

*b*

*b*

·

*p*

Thus, all resonance states from GTR (*k* = 0) to PR3 (*k* = 3) are described by one formula (3).

#### 3. Results

The energies of five charge-exchange resonances — AR, GTR, PR1, PR2, and PR3 — calculated in the microscopic approach for tin isotopes
*E*

##### Table 1

As shown in Figure 1 (a) the experimental data for excitation spectra in
*t*)
*E
*) for the

*E*x
– is the excitation energy. Unfortunately, direct measurements of the strength function S(

*E*x
) have not been performed, but the data on counts shown in Fig. 2a are proportional to the partial data on the function S(

*E*x
).

As shown in Figure 2 the calculated energy differences *E*
*E*
*k* = 0 in Eq. (3)) and pygmy resonances (*k* = 1, 2, 3) as functions of the mass number *A*. As is seen in Fig. 2, the microscopic calculations for the PR1 pygmy resonance as compared to the experiment give the best accuracy: the corresponding standard deviation is δ*E* = 0.31 MeV (see Table 1) as compared to δ*E* = 0.53 MeV for calculations by Eq. (3). For the PR2 pigmy resonance, the calculation by Eq. (3) with δ*E* = 0.26 MeV is more accurate than the microscopic calculation with δ*E* = 0.36 MeV. The largest discrepancy between the microscopic calculations and experiment is observed for
*E* = 0.33 MeV is more accurate than the calculation by Eq. (3) with δ*E* = 0.50 MeV. Nevertheless, the calculations by two methods on average satisfactorily describe the experimental data.

#### 4. Conclusion

The first microscopic numerical and semi-classical calculations have been performed for ten tin isotopes with the mass numbers *A* = 112, 114, 116, 117, 118, 119, 120, 122, 124, and 126, for which experimental data exist [6]. Charge-exchange resonances: giant Gamow–Teller (GTR), analog (AR) resonances, and the so-called “pygmy” resonances (PR), which are lying below GTR, have been studied in the self-consistent theory of finite Fermi systems (TFFS). Microscopic numerical calculations and semi-classical calculations are presented for nine tin isotopes
*t*)Sb charge-exchange reaction at the energy *E*(
*E*
*E*
*E*
*E*
*E*
*A *in heavy nuclei indicating the restoration of Wigner SU(4)-symmetry [8]. The calculated Δ*E*
*E *
*E*
*E*
*E*

The charge-exchange strength function of the