Side-feeding Times Research Articles

High spin states of the normally deformed bands of Y83

Level lifetime and side-feeding time measurements were performed on the excited states of the normally deformed bands of Y83 using the Doppler-shift attenuation method (DSAM). The high spin states of Y83 were populated using the fusion-evaporation reaction Ni58(S32,α3p)Y83 at 135 MeV. Twenty-two level lifetime and side-feeding times were determined in most of the cases by comparing the line shapes gated with transitions above and below the state under study. Quadrupole moments determined from lifetime measurements are in the range 1.1-3.1 eb, and are similar to the ones found for some of the neighboring nuclei. The measured side-feeding times were compared with predictions made by simulations carried out with the Gammapace code. The results were in agreement with the experimental values by assuming reduced transition probabilities of the collective transitions in the continuum region, lying in the range 40-80 W.u. The discrete excited states were studied with paired cranked Nilsson-Strutinsky-Bogoliubov (CNSB) calculations carried out for the first time for an A≈80 nucleus. Unpaired cranked Nilsson-Strutinsky (CNS) calculations were used to specify configurations and study the band crossings. The measured |Qt| values show a general agreement with CNSB calculations. Cranked shell model analysis evinced that the smallest quadrupole moment appears at the sharpest band crossing of the bands studied and CNSB calculations show an increase of the deformation thereinafter. (Less)

AhKin: A modular and efficient code for the Doppler shift attenuation method

We present a set of programs for measuring lifetimes τ of nuclear states by the Doppler shift attenuation method (DSAM). The algorithms are based on the analysis of a probabilistic model of the processes occurring during a DSAM experiment. This analysis allows us to formulate the calculation of the theoretical lineshape as the application of an integral transform that converts the probability density of the cascade time (the time elapsed from nucleus creation to state decay) into the probability density of the (scaled) photon energy in the laboratory reference frame. The kernel of this integral transform, which encapsulates information related to the processes of nuclei stopping and photon detection, is independent of the state decay process, and hence needs not be recalculated on every trial of a candidate τ-value, allowing for fast computation of theoretical lineshapes. Further efficiency is gained by using algorithms that approximate continuous random variables by suitably chosen discrete ones. These codes were used to measure the lifetimes and sidefeeding times of the excited states of the normally deformed bands of 83Y (Rodriguez, et al. 2019) finding for all states good agreement between the experimental lineshape and the best-fitting theoretical one. Program summaryProgram Title: AhKinProgram Files doi:http://dx.doi.org/10.17632/559kb329p2.1Licensing provisions: MITProgramming language: C++Nature of problem: Measurement of lifetimes of excited nuclear states by the Doppler shift attenuation method. This involves simulating the measured energy spectrum (lineshape) of photons emitted in transitions between excited states of a nucleus traveling in a stopping material. The reduction in time of the nucleus velocity relates the state lifetime to the observed Doppler shift of the photon’s energy. The measured lifetime is assumed as the value producing the theoretical lineshape that best approximates the experimental spectrum.Solution method: A probabilistic model allows to formulate the computation of theoretical lineshapes as the evaluation of an integral transform that converts the probability density of cascade times to the Doppler-shifted photon energy spectrum. The kernel of this integral transform is independent of the state decay process, and need not be recalculated for every trial of a candidate lifetime value, permitting swift computation of lineshapes. Additional algorithmic efficiency is obtained by approximating continuous random variables by discrete ones.

Side feeding patterns and nuclear lifetime determinations by the Doppler shift attenuation method in (α,nγ) reactions

$\ensuremath{\gamma}$ rays were measured at several angles in both singles and coincidence mode in the $^{119}\mathrm{Sn}$($\ensuremath{\alpha},n\ensuremath{\gamma}$)$^{122}\mathrm{Te}$ reaction at 15 MeV on a thick target. Lifetimes of excited states in $^{122}\mathrm{Te}$ were determined from a Monte Carlo Doppler shift attenuation method (DSAM) analysis of the Doppler broadened lines shapes of $\ensuremath{\gamma}$ rays de-exciting the levels. A comparison of several deduced lifetimes with recent results obtained with the ($n,{n}^{\ensuremath{'}}$) reaction allowed us to validate the choice of a parameter used to calculate the contribution of the side feeding times. The ingredients of the DSAM line-shape analysis (stopping power, description of instrumental line shapes, and side feeding evaluation) are presented in some detail. It is concluded that with proper treatment of side feeding, a DSAM line-shape analysis of peaks in singles or coincidence spectra obtained following the ($\ensuremath{\alpha},n\ensuremath{\gamma}$) reaction is able to provide rather accurate values for the lifetimes of levels with low and medium spins.

High-spin structure of normal-deformed bands in84Zr

The reaction Ni-58(S-32,alpha2p) at E-lab=135 MeV was used to populate high-spin states in Zr-84. The complete GAMMASPHERE and MICROBALL arrays were used to obtain clean gamma-gamma-gamma line shapes to be analyzed by the Doppler shift attenuation method and to determine 27 lifetimes in the ground-state band and in two excited bands. Side-feeding times were also measured by comparing the line shapes gated with transitions above and below the state under study. The deduced electric quadrupole moments for the ground-state band are consistent with a very slow reduction with frequency with values ranging between 2.4(3) and 2.0(1)e b. The negative-parity bands feature also an approximate constancy of quadrupole moment with values similar to those in the ground-state band. Cranking calculations agree with this behavior in both parity bands and suggest an interpretation of the upper states in the ground-state band as part of a very slowly terminating band. Shell-dependent cranked Nilsson calculations explain a fourth gamma cascade as pertaining to a noncollective structure terminating at I=20(+). (Less)

New Approach to Doppler Lifetime Measurements

The modified procedure of RDM and DSAM data analysis applied to lifetime measurements in 119I presented. The main points are: the Recoil Distance Doppler Shift Attenuation Method, the evaluation of side-feeding time, and self-calibration of stopping-power parameters by “semi-thick” target method.

Coincidence Doppler shift lifetime measurements in 73,74Se and 74Br using the EUROBALL Cluster cube array

Subpicosecond lifetimes of high spin states in the rotational nuclei 73Se, 74Se and 74Br have been measured using the 58Ni +19F compound reaction and the Doppler Shift Attenuation method. Six EUROBALL Cluster detectors arranged in cube geometry allowed us to select the relevant transitions in γγ coincidence mode. The high counting statistics achieved in this setup also facilitated the determination of average sidefeeding times, which were found to agree rather well with the results of Monte-Carlo calculations of the particle and γ-ray evaporation process. The deduced quadrupole strengths and deformations are compared with the results of previous measurements and the predictions of Cranked Shell Model calculations. In 74Br, a large and constant prolate deformation of β2= 0.37(1) was found for the presumed 4+ and 3− two-quasiparticle bands.

Rotational bands in77Rb: Spectroscopy near theZ=38deformed shell gap

The $\ensuremath{\gamma}$ decays of high spin states in ${}^{77}$Rb populated in the reaction ${}^{40}$Ca${(}^{40}$Ca,$3p)$${}^{77}$Rb were studied with the EUROGAM I $\ensuremath{\gamma}$-ray spectrometer at Daresbury Laboratory, in conjunction with the recoil mass separator. The data were used to extend or establish three positive parity and five negative parity bands in ${}^{77}$Rb. Level lifetimes and sidefeeding times were then measured with the NORDBALL $\ensuremath{\gamma}$-ray spectrometer, using the Doppler shift attenuation method. A very detailed level scheme including many weakly populated states was established and the bands were observed over large spin ranges. The deduced lifetimes demonstrate the high collectivity of the excited states and are consistent with their having large prolate deformations. The structures of the bands and their crossings are discussed in relation to the large shell gap at prolate deformation ${\ensuremath{\beta}}_{2}\ensuremath{\approx}0.4$.

Transition strengths and multiple band structure in 82Sr.

High-spin states in $^{82}\mathrm{Sr}$ were studied using the $^{56}\mathrm{Fe}$${(}^{29}$Si,2pn) reaction at 95 MeV with a thick 78 mg/${\mathrm{cm}}^{2}$ natural Fe (92% $^{56}\mathrm{Fe}$) target. Prompt \ensuremath{\gamma}-\ensuremath{\gamma} coincidences were measured using three Compton-suppressed Ge detectors at 90\ifmmode^\circ\else\textdegree\fi{} relative to the beam and two at 30\ifmmode^\circ\else\textdegree\fi{}. Directional correlation of oriented nuclei ratios were determined from the 30\ifmmode^\circ\else\textdegree\fi{}-- 90\ifmmode^\circ\else\textdegree\fi{} coincidences to assist in assigning spin changes. Nine new states were found, along with 38 new transitions. The Doppler-shift attenuation method was used to determine the mean lifetimes of 22 states in $^{82}\mathrm{Sr}$. The continuum side feeding times into 10 states were determined by comparing the decay line shapes in coincidence with transitions above and below the state under study. The average transition quadrupole moment of 2.8(2) e b in the ground state band of $^{82}\mathrm{Sr}$ would correspond to a relatively large axial quadrupole deformation of ${\mathrm{\ensuremath{\beta}}}_{2}$=0.33, in agreement with theoretical predictions. The excited ${2}^{+}$ band has a higher moment of inertia but a lower transition quadrupole moment of 2.4(2) e b. In the negative-parity bands the quadrupole moment falls from about 3 to 2 e b with increasing spin.

Transition strengths in 79Rb.

High angular momentum states in $^{79}\mathrm{Rb}$ were populated via the $^{63}\mathrm{Cu}$${(}^{19}$F,2pn${)}^{79}$Rb and $^{65}\mathrm{Cu}$${(}^{18}$O,4n${)}^{79}$Rb reactions. The 65 MeV $^{19}\mathrm{F}$ and 65 MeV $^{18}\mathrm{O}$ beams were provided by the Florida State University FN Tandem accelerator. Prompt \ensuremath{\gamma}-\ensuremath{\gamma} coincidences were measured for both reactions. Two additional \ensuremath{\gamma} cascades have been assigned to $^{79}\mathrm{Rb}$, including a new high-excitation structure dominated by dipole transitions. Firm spin assignments were made for the first time for a number of states by means of directional correlation ratios and an angular distribution measurement using the $^{63}\mathrm{Cu}$${(}^{19}$F,2pn) reaction. The Doppler-shift attenuation method was used to determine lifetimes for states and their respective side-feeding times in both the yrast positive-parity and yrast negative-parity states. Transition quadrupole moments were deduced from the transition strengths and compared with those predicted by Woods-Saxon cranking calculations. The energy spacings and mixing ratios were compared with particle-rotor calculations.

Second minimum lifetime measurements in 133Nd and 137Nd.

The quadrupole moments (${\mathit{Q}}_{0}$) of the highly deformed, second minimum bands in $^{133}\mathrm{Nd}$ and $^{137}\mathrm{Nd}$ have been extracted from mean lifetime measurements using the Doppler shift attenuation method. The reactions $^{105}\mathrm{Pd}$${(}^{32}$S,2p2n${)}^{133}$Nd at 152 MeV and $^{104}\mathrm{Ru}$${(}^{36}$S,3n${)}^{137}$Nd at 145 MeV were used. A standard centroid shift analysis was carried out in both cases, which gave values of ${\mathit{Q}}_{0}$=(6.0\ifmmode\pm\else\textpm\fi{}0.7)e b and (4.0\ifmmode\pm\else\textpm\fi{}0.5)e b for $^{133}\mathrm{Nd}$ and $^{137}\mathrm{Nd}$, respectively, corresponding to axial prolate deformations of ${\mathrm{\ensuremath{\beta}}}_{2}$\ensuremath{\simeq}0.33 and \ensuremath{\simeq}0.22. A line-shape analysis was also carried out for $^{133}\mathrm{Nd}$ to check against the possible effect of sidefeeding. The result was ${\mathit{Q}}_{0}$=(6.7+0.7)e b, with sightly slower sidefeeding times corresponding to ${\mathit{Q}}_{\mathrm{sf}}$\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\simeq}5.3e b. The results are in good agreement with the predictions of total Routhian surface calculations, and are discussed in the context of other highly deformed bands in the A=130--140 mass region.

Side-feeding times in even dysprosium isotopes

The continuum γ-decay in the isotopes 152–158Dy after heavy-ion compound reactions is studied by means of the Monte Carlo simulation. Side-feeding times, γ-ray multiplicities and intensities and E2 spectra are discussed. Rotational damping is included in the analysis. The dependence of the feeding times of yrast states on the parameters controlling the γ-decay is analyzed.

Side-feeding times and level lifetimes measured in the reaction 54Fe( 32S, 3p) 83Y

We have performed recoil-distance and Doppler-shift-attenuation lifetime measurements in the reaction 54Fe( 32S, 3p) 83Y at 103–107 MeV beam energy. By analyzing the Doppler-broadened line shapes of the 964 keV 21 2 + → 17 2 + yrast transition in coincidence with feeding and depopulating transitions, the average side-feeding time and lifetime of this state have been deduced as τ F = 0.6(2) ps and τ = 0.62(10) ps, respectively. A similar analysis of the 811 keV 17 2 +→ 13 2 + transition gave values of τ F = 0.65(25) ps and τ = 1.5(2) ps, respectively for the 17 2 + yrast state. Feeding times of the higher transitions in the positive-parity yrast band have been estimated from their Dopplerbroadened lineshapes measured in coincidence with depopulating transitions only. The feeding times are compared with the results of Monte Carlo calculations of the time development of the continuum γ-ray flux, and a damping width of 2–3 MeV has been deduced. The measured level lifetimes support the regular band structures with the deformation β 2 = 0.33 previously inferred from the transition energies.

Two-quasiparticle bands in72Br

High spin states in the doubly odd nucleus72Br were investigated via the reaction58Ni(16O,pn) at 52–65 MeV beam energy. A multi-element detector system consisting of ten Compton supressed Ge detectors (OSIRIS) and two NE213 neutron detectors was used to establish the yrast bands up to 5 MeV excitation energy and probable spins of 15+ resp. 14−. The lifetimes of 12 states and lifetime limits of four states were measured with the recoil distance method, among them four 0.5–3.1 ns isomers. Doppler broadened line shapes obtained in an additionalγγ-coincidence experiment via the reaction40Ca(36Ar, 3pn) at 125 MeV revealed further lifetimes and (very short) side feeding times. Three rotational bands were established with deformation parameters ¦β2¦≈0.3 and moment of inertia parameters\(\tilde f\)/ħ2=36 MeV−1 (Kρ=1−) resp. 23 MeV−1; their quasi-particle configurations are being discussed.

Lifetime measurements in 120Xe, using a coincidence plunger technique

Lifetimes and side feeding times in 120Xe were measured using the recoil-distance Doppler-shift technique, taking γ-singles spectra as well as γγ-coincidences. The reaction 110Cd( 13C, 3n) 120Xe was used at a bombarding energy of 56 MeV. Lifetimes of 1.0 (5) ps and 1.9 (6) ps respectively were obtained for the 10 1 + and 8 1 + states from their decay curves taken in coincidence with the strongest discrete feeding transitions. Using these lifetimes, we determined side feeding times of 2.2(13)ps for the 10 1 + state and 3.5 (26) ps for the 8 1 + state, from their decay curves taken in coincidence with transitions below these levels. Decay curves taken from γ-singles spectra yielded side feeding times of 2.9 (14) ps for the 10 1 + state and 4.1 (28) ps for the 8 1 + state.

Line-shape analysis of high spin states: Collectivity in 166Yb.

The Doppler-shift attenuation method was used to measure lifetimes of yrast states in /sup 166/Yb. Three different stopping materials were used and consistent results were obtained over a large range of spins. Values of tau range from 1.20(10) ps at 18/sup +/ to 0.05(1) ps at 34/sup +/. The B(E2) values steadily decrease from 200 to 120 single particle units as the spin increases above 24h-dash-bar. This loss of collectivity is likely to reflect a change toward triaxial shapes. The side-feeding times to these states are longer than the inband feeding times.

Lifetime measurements of high-spin states in 166Yb.

The Doppler-shift attenuation method was used to measure lifetimes of yrast states in $^{166}\mathrm{Yb}$. Values of $\ensuremath{\tau}$ range from 0.16(2) ps at ${24}^{+}$. to 0.05(1) ps at ${34}^{+}$. The $B(E2)$ values decrease from 240 to 120 single-particle units in this spin range, indicating a loss of collectivity which likely reflects a change of the nucleus towards triaxial shape. The side-feeding times are consistent with rotational cascades having moments of inertia 25% larger than the yrast sequence or $B(E2)$ values around 60 single-particle units.

Yrast transition strengths and band structure of 75Br.

High spin states in $^{75}\mathrm{Br}$ were investigated in the reactions $^{62}\mathrm{Ni}$${(}^{16}$O,p2n) and $^{66}\mathrm{Zn}$${(}^{12}$C,p2n). By means of \ensuremath{\gamma}\ensuremath{\gamma}- and \ensuremath{\gamma}-neutron multiplicity coincidence measurements, rotational bands of both parities were extended up to 7 MeV excitation energy and spin I=(33/2). The lifetimes of 17 yrast states were determined with the recoil distance and Doppler shift attenuation methods; the spin dependence of the side feeding time was also measured. The data have been analyzed in terms of the Strutinsky-Bogolyubov cranking model with a Woods-Saxon average potential. The first crossing observed in the negative parity bands is attributed to the alignment of a ${g}_{9/2}$ proton pair; the next irregularity which is also observed in the positive parity band is interpreted as the alignment of ${g}_{9/2}$ neutrons. The coexistence of prolate and oblate configurations at low spin and the change of nonaxial deformation with rotational frequency due to the polarization of the even-even core by the odd particle are discussed. The signature inversion visible in the negative parity bands as well as the changes in the signature splitting and reduction of B(E2) values at high spins may be related to a transition from \ensuremath{\gamma}<0\ifmmode^\circ\else\textdegree\fi{} to \ensuremath{\gamma}>0\ifmmode^\circ\else\textdegree\fi{} triaxial shapes.

Rotation-induced shape transitions in Dy nuclei

Lifetimes of states with spins up to 30ħ have been measured in the nuclei 156Dy, 157Dy, and ll58Dy using the recoil-distance technique together with inverse reactions of the type Mg( 136 Xe, x n) . The applied method, which benefited from the high velocities of the fusion residues as well as from improvements of the recoil-distance technique, allowed us to determine lifetimes and feeding times down to 0.1 ps. Below the first backbending the resultant B(E2) values in the ground-state band of 156, 158Dy increase faster with increasing rotational frequency than expected for rigid rotors, reaching values similar to those observed for the well-deformed neutron-rich Dy isotopes. In contrast to this, the E2-transition probabilities between high-spin states are clearly retarded. The retardation gradually evolves from the rotation alignment of nucléons and indicates deformation changes most likely towards a triaxial shape. From the analysis of the side-feeding times of the high-spin yrast states it could be furthermore deduced that the E2 component of the preyrast γ-decay stems from transitions along highly collective bands.

Side feeding times to yrast states of158Dy in26Mg(136Xe, 4n)158Dy

Side feeding times to the yrast states of158Dy were analyzed and compared with Monte Carlo calculations. It is found that B (E2) value's in pre-yrast stretched E2 transitions are about 80% of the rigid rotor prediction. Average multiplicities and corresponding transition energies are also calculated and compared with the experimental data.

Use of the (p,γ) reaction on semi-thick targets in the spectroscopy of odd mass nuclei

Singles $\ensuremath{\gamma}$-ray angular distributions obtained from the ($p,\ensuremath{\gamma}$) reaction on $^{56}\mathrm{Fe}$, $^{62}\mathrm{Ni}$, $^{66}\mathrm{Zn}$, and $^{68}\mathrm{Zn}$ targets having a thickness of 3-5 mg/${\mathrm{cm}}^{2}$ are used to evaluate the statistical tensors for the alignment of the low-lying levels of $^{57}\mathrm{Co}$, $^{63}\mathrm{Cu}$, $^{67}\mathrm{Ga}$, and $^{69}\mathrm{Ga}$. The results show that these levels acquire a relatively strong alignment which depends only on the spin of the low-lying state. This fact makes the method suitable for spectroscopic investigation of odd mass nuclei. It has also been found that the observed Doppler shift of the transition in these nuclei can yield information on the lifetimes of the excited states upon the assumption of a side feeding time of 20 fs for the continuum $\ensuremath{\gamma}$ cascades. The method is illustrated with the examination of the level properties of the $^{69}\mathrm{Ga}$ nucleus.[NUCLEAR REACTIONS $^{56}\mathrm{Fe}$, $^{62}\mathrm{Ni}$, $^{66}\mathrm{Zn}$, $^{68}\mathrm{Zn}(p,\ensuremath{\gamma})$, $E=2.0\ensuremath{-}4.0$ MeV. Measured $I\ensuremath{\gamma}(\ensuremath{\theta})$. $^{57}\mathrm{Co}$, $^{63}\mathrm{Cu}$, $^{67}\mathrm{Ga}$, $^{69}\mathrm{Ga}$ deduced statistical tensors for alignment, side feeding time. $^{69}\mathrm{Ga}$ levels deduced $J$, $\ensuremath{\delta}$, $\ensuremath{\tau}$. Enriched targets, Ge(Li) detectors.]