RATIO OF TRANSITIONS IN SOME OF SAMARIUM ISOTOPES

Samarium isotopes (Z=62) lies in the traditional rotational to transitionalspherical region that occurs at the range of deformed nuclei. Gamma ray ( ) 1 / 2 M E δ mixing ratio and ( ) 2 / 0 E E X ratio for selected transitions in Sm148154 are calculated in the frame work of proton-neutron interacting boson model (IBM-2). The results obtained for Samarium isotopes are reasonably in a good agreement with the previous experimental results.


Introduction
Naturally occurring samarium is composed of 4 stable isotopes,Sm144, Sm150, Sm152, Sm154 and three radioisotopes Sm147, Sm148 and Sm149, with Sm152 being the most abundant (26.75%) [1] .These isotopes Z=62 and N=82 to 92 are well abrupt changes in nuclear properties between almost spherical in N=82 to well deformed in N=92 [2].So Sm isotopes have provided a useful testing ground for nuclear structure calculations.
The Interacting Boson Approximation (IBA) model [3][4] has been remarkably successful in the description of the low-lying collective states in many medium to heavy even-even nuclei.The neutron-proton version of the interacting boson model (IBA-2), later suggested by Iachillo and Arima [5] which distinguishes between neutron ) (ν and proton ) (π , is used in the present work, a full description of the IBA-2 is found in reference [6].The Hamiltonian operator in IBA-2, which been used to calculated the energy level and hence the gamma transitions matrix elements, has three parts, one for proton bosons, one for neutron bosons and one that describes the interaction between unlike bosons: (1) The Hamiltonian generally used in phenomenological calculations can be written as ,in equation ( 2) which correspond to interaction between like-boson, are sometimes included in order to improve the fit to experimental energy spectra.They are of the form This work aimed at two thinks: first, to give the Hamiltonian of IBA-2 in terms of the formalism; second is to study the transitions probability and mixing ratio of Sm isotopes by use of this Hamiltonian.

The Calculation and Results
The Ichillo and Arima in their original interacting boson approximation give the M1 operator in the restricted case of U(5) dynamic symmetry [3] and as well as the general case used by Sholton [9].How ever, even when starting with general operator, they derived the E2 / M1 mixing ratio by neglecting the term which break the SU(3) symmetries.It follows that the reduced mixing ratio is given by the same simple formula which contains only one parameter and the initial and final spin, which can be derived as fallows: In IBA-2, the E2 , transition operator is given by,

. After calculated the E2 matrix elements we lock after the M1 matrix elements as fallows:
The M1 operator obtained by letting 1 = l in the single boson operator of the IBM-1 and can be written as where ν π g g , are the boson g- factors in units of N µ and . This operator can be written as [ ] The first term on the right hand side ,in the above equation, is diagonal and therefore for M1 transitions the previous equation may be written as The direct measurement of B(M1) matrix elements is difficult normally, so the M1 strength of gamma transition may be expressed in terms of the multipole mixing ratio which can be written as [11 where

Discussion and Conclusions
Good agreements with the experimental energy for the low laying levels was obtained and according to that the mixing ratios were calculated after calculate E2 and M1 matrix elements.All the experimental and theoretical mixing ratios for Sm isotopes indicate a small M1 components which means that in the band-mixing transitions, M1 components is almost forbidden.

In the calculation of
δ it is found that there is a great effect of the Majorano parameter 2 ξ on the value and sign of E2 and M1 matrix elements.However, an acceptable overall agreement between the experiment and theory were obtained as shown in table-2.The lack of agreement indicates that the perturbation expansion of angular momentum works well for strongly deformed nuclei and does not describe nuclei in the transitional region.The model was not able to produce the sing of the mixing ratio of the transition from gamma to ground band.
The present study provides further support for the idea of the co-existence of spherical vibrator in Sm148 to deformed-rotor characteristics in the N=88 isotones of Sm, Gd and Nd as been shown by Gupta and Kumar [19] The E0 quantities predicted by the two theories for 03+ states were on the whole in poor agreement with experiment.In general we note that the E0 transition matrix elements provide a highly critical test of nuclear model.Furthermore, the microscopic characters of the ground states and the excited 0+ states in Sm150-152 would appear to be sufficiently complex to eliminate any description of them in the term of simple model.
ρ correspond to π (proton) or ν (neutron) bosons.The second term denotes the main part of the boson-boson interaction, i.e.
between two states of the same spin and parity by transferring the energy and zero unit of angular momentum.Thus E0 has no competing gamma ray.These transitions are different from zero only in the case where the transition is accompanied by the nucleus surface change.For example in the nuclear models where the surface is assumed to be fixed E0 transitions are strictly forbidden.Electric monopole transitions can occur not only in 0+---0+ transition but also, matrix elements.The results of the calculation are listed in table-3.