Multipole collectivity inEr168from inelastic scattering

Description of low-lying vibrationalK ??0+ states of deformed nuclei in the quasiparticle-phonon nuclear model

“…There are three K~=4 + states in 172yb which are not however observed in the (ec~') reaction [26]. The calculated energies of the 4 + states are 0.15-0.30 MeV as less as the experimental ones.…”

“…The B (E 3) values shown in Table 3 are taken from [26] where the B(ISE3) values have been determined in the (a c() reaction; they somewhat differ from the B(E3) values obtained in [31] from the Coulomb excitation. The B(E 3) values calculated by us are between the value obtained in E26, 31] and more close to the values in [31].…”

“…The coupling between the vibrational and rotational motion will be neglected. Experiments [26] on inelastic scattering of e particles made it possible to study the isoscalar E2-strength distribution.…”

B(IS4; 0 GS + ?4 ? + ) systematics in rare-earth nuclei: SUsdg (3) description

“…Before proceeding further it should be mentioned that the iso-scalar hexadecupole mass transition density B(IS4) is defined as B(IS4; (0os~4m+ +) = {Ir4y4(g2)p(r)r2drdg?} 2, where m=0 for GS-band and 2 for ?,-band and p (r) is the transition density [4,5]. With the scale factor Z/A and the assumption that mass and charge distributions coincide, the B (IS4)'s will be numerically same as (the isoscalar part of) B(E4)'s [4,5].…”

“…2, where m=0 for GS-band and 2 for ?,-band and p (r) is the transition density [4,5]. With the scale factor Z/A and the assumption that mass and charge distributions coincide, the B (IS4)'s will be numerically same as (the isoscalar part of) B(E4)'s [4,5]. Assuming that the transition density p (r) has the same form (say Woods-Saxon) as the nuclear potential and carrying out coupled channel analysis together with y-vibrational or asymmetric rotor model, the By (IS4) values are deduced from scattering data (similarly fl4'S derive from B(IS4; (0~s~4as)).+ + In order to describe the above By (IS4) data, the sdglBM formalism given in [3] for the study of f14 systematics is extended to include: (i) a more realistic multi-j shell mapped (instead of the single-j shell version of the Otsuka, Arima and Iachello (OAI) mapping [6] employed in [3]) hexadecupole transition operators (TE4; p = g for proton bosons and v for neutron bosons) in proton, neutron spaces; (ii) derivation of exact expression for E4 matrix elements connecting members of GS-band to y-band in the S Usdg (3) limit (instead of using the Coherent State formalism [7,8]) and taking large-N limit.…”