Identification of spin relaxation following α-decay in odd-Anuclei

Abstract

A novel graphical method has been devised for [A + 4] (J P ) α −→ A * (J 1 ) γ −→ A (J 2 ) decay, in odd-A nuclei, when J P < J 1 , to determine whether spin relaxation in the state of spin J 1 has occurred. For a short lived excited daughter state A * of spin J 1 , its populated magnetic substates, following α-decay from a parent nucleus [A + 4] of spin J P , should be restricted to those of value |M| J P (when J 1 > J P ). However, for longer lived excited states, spin relaxation allows population of J P < |M| J 1 substates. The statistical tensors B 2 and B 4 (or population alignment coefficients) of Rose and Brink can be determined from the measured (non-zero) Legendre polynomial coefficients. These measured B 2 and B 4 can be compared with their theoretical counterparts both for the case when |M| J P and for the case when |M| J 1 . It is then readily apparent, from a graphical examination, whether spin relaxation has occurred or not. The same statistical tensors B 2 and B 4 , also allow one to analyse α-γ directional angular correlations and α-γ linear polarization angular distributions simultaneously, rather than as different data sets. The technique has been applied to the case of 219 Rn J P = 5/2 + α −→ 215 Po * J 1 = 7/2 + γ =271 keV − −−−−−→ 215 Po 9/2 + decay. Spin relaxation of the 271 keV state (T 1 / 2 ≈ 0.2 ns) allowing population of substates with |M| 7/2, is required to satisfactorily fit the published data. The population of the M = ±7/2 substates due to spin relaxation is estimated to be less than 20% of the total, equally split between the two.

Multipole mixing ratios and substate populations in Rn-219

“…The theoretical coefficients, a , K of α−γ angular correlations can be factored into two parts [6,8,10]. a B population gamma decay 2.1…”

“…It has been shown [6] that for longer lived states of spin J , 1 spin relaxation can occur, where the quadrupole moment rotates to try to align with internal electric field gradients. The symmetry of the quadrupole interaction retains the alignment condition but, the torque on the system produces a precession of the angular momentum vector such that the projection of angular momentum J 1 onto the original quantization axis can change.…”

“…A recent study [6] has shown how (α−γ) angular correlations can be analysed in order to investigate whether spin relaxation has occurred. Although this procedure has been carried out for all decays in this study, only the 127 keV state is believed to have undergone spin relaxation.…”

Substate populations of spin-relaxed J≤5/2 states determined from (α–γ) angular correlation coefficients

“…(3), the sum over M is taken from À J P to þJ P if J P oJ 1 , since the projection of orbital angular momentum onto the quantization axis is zero. However, for a relatively long lived state ðT 1=2 Z 10 À 11 sÞ spin relaxation allows M to run from À J 1 to þJ 1 [3].…”

“…More recently spin relaxation has been identified [3] in the odd-A nucleus 215 Po. The 271 keV (J 1 ¼7/2 þ ) excited state of 215 Po (T 1/2 $ 0.2ns) was shown to undergo spin relaxation, following α-decay from the ground state of 219 Rn (J P ¼5/2 þ ), before γ-decay to the ground state (J 2 ¼ 9/2 þ ).…”