Population Of Magnetic Substates Research Articles

Magnetic substate population in [formula omitted] inelastic scattering

Using the λ-ray recoil method we have measured the spin alignment for the single 2 + excitation in 12C+ 12C inelastic scattering over the energy range 19⩽ E cm ⩽55 MeV. The angular distribution of the magnetic substate population has been obtained. As quantization axis for the description of the magnetic substate has been chosen the direction of the center-of-mas scattering angle of a decaying nucleus. The all-over behavior of the angular distribution is satisfactorily reproduced by a simple DWBA calculation.

Polarization studies of H(2p) charge-exchange excitation: H+-Ar collisions.

Alignment and orientation for H(2p) excitation in ${\mathrm{H}}^{+}$-Ar collisions have been measured for incident proton energies of 1.5 and 3 keV, and in the range of scattering angles between 0.5\ifmmode^\circ\else\textdegree\fi{} and 3.5\ifmmode^\circ\else\textdegree\fi{}. From the experimental results the relative population of magnetic substates H(2${p}_{0}$) and H(2${p}_{\ifmmode\pm\else\textpm\fi{}1}$) is extracted. The observed magnitude of the H(2${p}_{0}$) excitation suggests that, in addition to a 3d\ensuremath{\sigma}-3d\ensuremath{\pi} rotational coupling, a 3d\ensuremath{\sigma}-4p\ensuremath{\sigma} radial coupling is effective.

Energy and projectile dependence of nuclear alignment in fusion-evaporation reactions

Nuclear alignment attenuation coefficients of excited levels in 67Ga have been measured via the reactions 64 Zn + α and 57 Fe + 12 C for incident energies between 9 and 22 MeV and 32 and 48 MeV, respectively. The data were deduced from angular distributions of four pure electric quadrupole transitions in 67Ga. For the heavy-ion induced reaction a slight decrease of alignment with incident energy has been observed while there is a strong energy dependence of nuclear alignment for the α-induced reaction due to the feeding mechanism. The attenuation coefficients are consistent with the Gaussian magnetic substate population hypothesis except where direct and cascade feeding compete with comparable intersities.

High spin states in 67Ga

The nucleus 67Ga has been studied through the reaction 57Fe( 12C, pnγ) 67Ga at E 12 c = 40 MeV. New levels above 4 MeV excitation energy have been found and nuclear properties of these states are proposed from investigations of prompt γ-rays using in-beam γ-spectroscopic techniques. Comparison between the ground state sequence in 66Zn and the favoured states of positive parity up to J π = 25 2 + in 67Ga suggests that the latter can be explained in terms of coupling a g 9 2 proton to the 66Zn core. A second collective band of positive parity is proposed to be based on a configuration [( f 5 2 ) J≠O 2π g 9 2 ] 15 2 + . Results on magnetic substate populations of nuclear states formed in different heavy-ion induced reactions compiled. The α 2, α 4 combinations are consistent with the assumption of Gaussian distributed substate populations within the experimental errors.

Spin-alignment attenuation factors in mass 61–67 nuclei populated by ( α, n) and ( α, p) reactions

Gamma-ray angular distributions for 39 E2 transitions in A = 61–67 nuclei, excited in ( α , n) or ( α , p) reactions, are collected from the literature and reduced to spin-alignment attenuation factors α 2 and α 4 . The validity of the prediction for α 2 from statistical compound nucleus reaction theory is investigated. Also the sensitivity of this prediction to the optical-model parameters is examined. The present data support the rule 0 ⩽ α 4 ⩽ α 2 , but contradict the assumption of a Gaussian shape for the population of magnetic substates.

Measurement of spin-alignment of excited12C2+ nuclei in interactions of16O with12C usingγ-decay in flight

Measuring energy spectra of nuclei afterγ-decay of excited states in flight the spin alignment of12C2+ states has been measured. Inelastic scattering,16O(16C,12C2+)16O and the reaction12C(16O,12C2+)16O leading to12C2+ (4.43 MeV) state have been studied. Characteristic line shapes of the12C2+ peak were observed using a Q3D magnetic spectrometer. The magnetic substate (m-states) population has been deduced from the spectra as function of reaction angle. A comparison of the measuredm-state population with reaction models shows that the first reaction is consistent with inelastic scattering although discrepancies remain. Discrepancies are also obtained if the reaction12C(16O,12C2+)16O is interpreted using a FRDWBA transfer calculation. At least 1/3 of the cross section can be attributed toα-transfer. A calculation which couples transfer and inelastic scattering channels seems to be necessary.

The polarisation degree of some prominent helium lines after collisional excitation by fast ions

The polarisation degree pi of some prominent helium lines has been measured after collisional excitation by H+, H2+, H3+ and He+ ions in an energy range from 100-1000 keV. It was the aim of this experiment to investigate the influence of the different ion structures on the relative population of magnetic substates at high impact velocities. The proton data are compared with the first Born approximation. The effect of resonance-radiation capture on the measurement of pi (31P-21S) has been reinvestigated. It is concluded that the intensities I/sub /// and Iperpendicular to which enter into the definition of the polarisation degree are differently affected by resonance trapping at low gas densities.

Nonstatistical population of magnetic substates of the(1s−12p−1)P11state in Al

We have measured the polarization of the $K{\ensuremath{\alpha}}^{\ensuremath{'}}$ [$(1{s}^{\ensuremath{-}1}2{p}^{\ensuremath{-}1})^{1}P_{1}$] to [$(2{p}^{\ensuremath{-}2})^{1}S_{0}$] x ray from an Al target following bombardment by various ion beams at several different incident energies. The polarization of the $K{\ensuremath{\alpha}}^{\ensuremath{'}}$ x ray is a measure of the ratio of the $2p$ substate populations ${\ensuremath{\sigma}}_{1}({M}_{L}=\ifmmode\pm\else\textpm\fi{}1)$ and ${\ensuremath{\sigma}}_{0}({M}_{L}=0)$ of the $^{1}P_{1}$ state. We compare our results with recent collision-theory calculations which predict nonstatistical substate populations for simultaneous $K$- and $L$-shell ionization.

DWBA Analysis of Magnetic Substate Populations of Residual Nucleus in the 11B(d, p)12B Reactions

DWBA Analysis of Magnetic Substate Populations of Residual Nucleus in the 11B(d, p)12B Reactions

Cross sections, angular distributions, and magnetic substate populations in theNa23(n,n′γ)reaction

Neutron inelastic scattering cross sections have been determined for six levels in $^{23}\mathrm{Na}$ over the incident neutron energy range 0.52 to 4.23 MeV by measuring the $\ensuremath{\gamma}$-ray production cross sections for 10 deexcitation $\ensuremath{\gamma}$ transitions in the $^{23}\mathrm{Na}(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction. $\ensuremath{\gamma}$-ray angular distributions from the first two excited levels were obtained at various incident neutron energies. From these, the magnetic substate populations were evaluated for the 0.440-MeV (${5/2}^{+}$) first excited level and the 2.078-MeV (${7/2}^{+}$) second excited level in $^{23}\mathrm{Na}$. Comparisons have been made between the distributions and magnetic substate populations calculated from compound-nuclear and direct-interaction theory, the former yielding better agreement in the interpretation of experimental results.NUCLEAR REACTIONS $^{23}\mathrm{Na}(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$, ${E}_{n}=0.52\ensuremath{-}4.23$ MeV; measured $\ensuremath{\sigma}({E}_{n},{\ensuremath{\theta}}_{\ensuremath{\gamma}})$; deduced $\ensuremath{\sigma}({E}_{n})$ and magnetic substate populations; calculated $\ensuremath{\sigma}({E}_{n},{\ensuremath{\theta}}_{\ensuremath{\gamma}})$, $\ensuremath{\sigma}({E}_{n})$, magnetic substate populations; CN and DWBA analysis; natural (Na) target.

Magnetic-substate population in inelastic heavy-ion scattering

Magnetic-substate population in inelastic heavy-ion scattering

Magnetic substate populations of product nuclei in the 11B(d, p) 12B reaction

Magnetic substate populations of product nuclei in the 11B(d, p) 12B reaction have been measured in an energy range E d = 1.3−3.0 MeV at recoil angles of θ R = 55°, 515° and 27°−37°. A static magnetic field (3 kG) was applied normal to the reaction plane to keep the nuclear orientation. Quadrupole effects on the implanted 12B in Ta were utilized to perturb the Zeeman splitting. NMR transitions were induced, and detected by the asymmetry change in the β-decay of 12B. From this information, the magnetic substate populations were determined, for the unique assignment of which the sign of the quadrupole interaction had to be known. For this purpose, a p−γ angular correlation was measured, which determined the alignment of the first excited state of 12B. A comparison of the present result with theoretical predictions is given, together with the resultant information about j-mixings in the 12B states.

Inelastic neutron scattering inF19

Measurements of $\ensuremath{\gamma}$ rays from the $^{19}\mathrm{F}(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$ reaction have been performed with 0.2-1.7-MeV incident neutrons. The measured 110- and 197-keV level excitation functions, magnetic substate populations, and $\ensuremath{\gamma}$-ray angular distributions are generally consistent with compound-nuclear calculations. Although the experimental values of the 197-keV level excitation function are also consistent with a 15% direct-interaction component, the corresponding magnetic substate populations and 197-keV $\ensuremath{\gamma}$-ray angular distributions are not sensitive to this component.[NUCLEAR REACTIONS $^{19}\mathrm{F}(n,{n}^{\ensuremath{'}}\ensuremath{\gamma})$, $E=0.2\ensuremath{-}1.7$ MeV; measured $\ensuremath{\sigma}(E)$, $\ensuremath{\sigma}(E=1.3$ MeV,$\ensuremath{\theta}$); deduced magnetic substate populations, calculated $\ensuremath{\sigma}(E,\ensuremath{\theta})$, magnetic substate populations; DWBA and CN analysis.]

Angular correlation study of the proton decay ofN14states below 11 MeV

Angular correlations of decay protons from 15 unbound $^{14}\mathrm{N}$ states below ${E}_{x}=11$ MeV were measured in the reaction $^{12}\mathrm{C}(^{3}\mathrm{He},p)^{14}\mathrm{N}({p}^{\ensuremath{'}})^{13}\mathrm{C}_{\mathrm{g}.\mathrm{s}.}$. Incident $^{3}\mathrm{He}$ energies of 12.0, 13.5, and 14.0 MeV were used in the various measurements. The decay protons (${p}^{\ensuremath{'}}$) were detected in coincidence with reaction protons ($p$) emitted at 0\ifmmode^\circ\else\textdegree\fi{} to the beam direction. The correlations were fitted to a theoretical expression containing adjustable parameters describing the $^{14}\mathrm{N}$ substate populations and the angular momentum coupling in the $^{13}\mathrm{C}+p$ system. Where two orbital angular momenta were allowed in the decay channel, generally only the lower allowed value was considered. Our results are compared with previous work and are shown to strengthen several existing ${J}^{\ensuremath{\pi}}$ assignments. New assignments are: 10.06 MeV, ${J}^{\ensuremath{\pi}}={3}^{+}$ or $J\ensuremath{\ge}4$; 10.81 MeV, ${J}^{\ensuremath{\pi}}={5}^{+}$. The $\frac{f\ensuremath{-}}{p}$-wave mixing in the decay of the 9.17-MeV ${2}^{+}$, $T=1$ state is consistent with previous $^{13}\mathrm{C}(p,\ensuremath{\gamma})$ experiments; for the 10.43-MeV second ${2}^{+}$, $T=1$ state, ${\ensuremath{\Gamma}}_{l=3}<(2.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3})\ensuremath{\Gamma}$. The measured magnetic substate parameters are compared with the predictions of a simple direct-interaction model of the ($^{3}\mathrm{He},p$) reaction. A recent weak-coupling model calculation of $^{14}\mathrm{N}$ levels is reviewed in the light of the new results.[NUCLEAR REACTIONS $^{12}\mathrm{C}(^{3}\mathrm{He},p)^{14}\mathrm{N}({p}^{\ensuremath{'}})^{13}\mathrm{C}(\mathrm{g}.\mathrm{s}.)$, $E=12.0,13.5,14.0$ MeV; measured $p$, ${p}^{\ensuremath{'}}$ coin., ${I}_{{p}^{\ensuremath{'}}}({\ensuremath{\theta}}_{{p}^{\ensuremath{'}}})$, ${\ensuremath{\theta}}_{p}={0}^{\ensuremath{\circ}}$. $^{14}\mathrm{N}$-deduced $J$, $\ensuremath{\pi}$, $\ensuremath{\delta}({l}_{{p}^{\ensuremath{'}}})$, channel spin, magnetic substate populations. Magnetic spectrometer, sequential reaction.]

Angular distribution of stretched E2 transitions for Gaussian substate population of side feeding in (particle, xn γ) reactions

In (particle, xn γ) reactions the population of magnetic substates of a given level of spin J in the ground state quasirotational band resulting from the preceding neutrons and gammas from outside the band (i.e. side feeding) can be described by a mixture of Gaussians of various widths. The resulting angular distribution of the stretched E2 (denoted E2 ) gammas with respect to the direction of the particle beam is analysed here. It is not approximated that an E2 transition from a Gaussian distribution of substates of level J produces a Gaussian distribution for the final level J−2. The ( A 2, A 4) results are discussed for a state populated by previous E2 transitions plus a single Gaussian side feeding. The results are extended to include side feeding producing substate populations of any mixture of Gaussians. A method of exact solution is given for cases where the experimental data are sufficiently accurate. The region of the ( A 2, A 4) space which can result from any mixture of Gaussian side feedings is derived. The results of various assumed substate populations of side feeding are compared to experiments by Newton et al. on 182W(α, 2n) 184Os, 165Ho( 11B, 4n) 172Hf and 159Tb( 14N, 5n) 168Hf. The comparison is quite satisfactory for single Gaussian side feeding of width σ = 2.8 for each level of spin J. The qualitative differences in the angular distributions for these experimental cases are caused by different experimental intensities of side feeding. For 74Ge(α, 2n) 76Se a width σ = 1.6+0.1 J gives good agreement with our experimental angular distributions of the transitions 10 → 8, 8 → 6, 6 → 4, 4 → 2 and 2 → 0. The angular distribution is also derived for a case where the population of substates increases with M.

Angular correlations in 23Na(p,γ)24Mg

The decays of two resonances in 23Na(p,γ)24Mg have been studied by γ–γ angular correlation methods. These resonances occur at proton energies of 1020 and 1318 keV and correspond respectively to levels in 24Mg at 12.671 and 12.957 MeV. In the latter case, the analysis of the data leads to an assignment of J = 1 to the level at 12.957 MeV. The angular correlation measurements confirm a previous assignment of J = 2 to the 12.671 MeV level and the information on magnetic substate populations obtained from the angular correlation analysis, together with a measurement of the angular distribution of the 12.671 to 8.86 MeV transition, yield an assignment of 2− to the 24Mg level at 8.86 MeV.

Alpha particles from the proton bombardment of light nuclei

Synopsis Resonances in the α -particle yield from proton bombardment of 23 Na, 27 Al, 31 P, and 35,37 Cl, were investigated in the energy range E p = 200 – 850 keV. Resonance energies, strengths, and the ensuing partial widths are reported. Angular distribution measurements yield spin and parity, formation mixing parameters, and/or magnetic substate population probabilities of several resonance levels. In the reaction 23 Na( p, α ) 20 Ne two new resonances were found, at E p = 743.3±0.4 and 845 ± 5 keV. The E p = 287, 338, 591, 743, 795, and 813 keV resonances have J π = (1 − , 2 + ), 3 − , 3 − , 2 + , (1 − , 2 + ), and 2 + , respectively. The E p = 591 keV resonances in the 23 Na( p, α ) 20 Ne and 23 Na( p, γ ) 24 Mg reactions correspond to two 24 Mg levels, differing 0.37 ±0.10 keV in excitation energy. At the three resonances in the 27 Al( p, α ) 24 Mg reaction, the magnetic substate population probabilities agree with those found from previous 27 Al( p, γ ) 28 Si work. The two resonances in the 31 P( p, α ) 28 Si yield curve, at E p = 618.7 ± 0.9 and 641 keV, have J π = (2+, 3 − ) and 1 − , respectively; the first resonance has not been reported earlier. No α particles resulting from the 35 Cl( p, α ) 32 S or 37 Cl( p, α ) 34 S reactions were observed.