A useful spectroscopic tool: The (7Li, 6He) reaction

Angular distribution measurements for the reactions ²⁴Mg(⁷Li, ⁶He)²⁵ Al and ⁵²Cr(⁷Li, ⁶He)⁵³ Mn at$\text{E(}{}^7\text{Li) = 34}$ MeV show that for angles less than 15°, the shapes of the measured angular distributions allow $\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ or $\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, and $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ or $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ final-state configurations to be distinguished when compared with finite-range DWBA calculations.     

The (p, 2p) reaction on 6Li

The differential cross section for the quasi-elastic scattering of protons on ⁶Li is derived in the impulse approximation. The nucleus ⁵He is not treated as a bound nucleus in the derivation. Instead, the n-α interactions $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$, $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ in the final state are included. Fits to the unknown vertex functions appearing in the expression obtained for the momentum distribution at the “ground state” of ⁵He are given, showing that the n-α $\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ interaction is important at the “ground state” of ⁵He. The consistency between the observed momentum distribution and the ⁶Li form factor at low momentum transfers is shown utilizing Elton's model.     

Study of 11B at high excitations with the 9Be(3He,p)11B and 9Be(α, d)11B reactions

The nucleus ¹¹B has been studied over the excitation energy range from 8.5 MeV to 21.5 MeV with the ⁹Be(³He, p)¹¹B / reaction at / E_{³He = 38 MeV}. The analogs of the parent states in ¹¹Be have been located at 12.56, 12.92, 14.40, 16.44, 17.69, 18.0, 19.15 and 21.27 MeV. A complementary measurement with the ⁹Be(α, d)¹¹B reaction at E_α = 48 MeV demonstrates that the 16.44, 17.69, 18.0 and 19.15 MeV resonances have rather pure isospin $\text{T}{}_{\mathrm{f}}\text{=}\text{3}\text{2}$. The 14.40 MeV state is a strongly isospin-mixed analog of the $\text{5}\text{2}{}^{\mathrm{+}}\text{1.78}\text{MeV}$ state in ¹¹Be. It is argued that spin S = 1 transfer is involved in the excitation of the 16.44 MeV state and its 3.887 MeV parent in ¹¹Be in a two-step stripping process. The $\text{T}{}_{\mathrm{f}}\text{=}\text{1}\text{2}$ states and the lowest three $\text{T}{}_{\mathrm{f}}\text{=}\text{3}\text{2}$ states are compared with the predictions of DWBA utilizing shell-model form factors. It is concluded that the $\text{T}{}_{\mathrm{f}}\text{=}\text{1}\text{2}$ strength is more strongly fragmented than is implied by the calculations of Teeters and Kurath.     

The differential cross section and polarization quantities in the 4He(d,p)n4He and 2H(α, n)p4He reactions

The differential cross section and the polarization quantities (T₁₁, T₂₀, T₂₁, T₂₂, P_γ') in the deuteron breakup reaction by an α-particle are calculated in the framework of the recently developed three-body model. All values are discussed under the incomplete kinematical condition. All polarization quantities are caused by the difference of the potential between $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ waves of the N-α interaction. Results of the calculation are compared with the available measurement of (i) the differential cross section and the deuteron vector analysing power in the ⁴He($\text{d}$, p)n⁴He reaction and (ii) the differential cross section and neutron polarization in the ²H(α, $\text{n}$)p⁴He reaction. The agreement with experiment is very satisfactory in each case. Among the tensor analysing powers of the deuteron the absolute value of T₂₀ is very large. Observables at the FSI peak corresponding to ⁵He_g.s. are discussed systematically in the energy region of 5.4–20 MeV of the incident deuteron in the ⁴He(d, p)n⁴He reaction. Although the differential cross section is not sensitive to the energy of the three-body resonance, the polarization quantities T₁₁, T₂₀, P_γ' are quite sensitive to it.     

Decay of the ground state and the 292+ isomer in 217Ac and g-factor measurements from perturbed α-particle angular distributions

The nucleus ²¹⁷Ac was studied using the ²⁰⁵Tl(¹⁶O, 4n), ²⁰⁶Pb(¹⁵N, 4n) and ²⁰⁹Bi(¹²C, 4n) reactions. The mesurements included αγ, γγ, α-ce and ce-ce coincidence experiments as well as γ-ray and α-particle perturbed angular distribution studies. Results are $\text{g(}{}^{\mathrm{217g}}\text{Ac}\text{) = + 0.85(1)}$ and $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(}{}^{\mathrm{<mtext>217</mtext><mtext>g</mtext>}}\text{Ac}\text{) = 69(4)}\text{ns}$, the shortest known α-decay of a ground state. ^217mAc decays mainly by a γ-cascade, but also by α-emission to the single-particle states $\text{π}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{,}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{,}\text{i}{}_{\mathrm{<mtext>f</mtext><mtext>13</mtext><mtext>2</mtext>}}$ of ²¹³Fr. Spins and parities of levels to the $\text{29}\text{2}$⁺ isomer at 2013 keV with $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 740(40)}\text{ns}$ and g = + 0.347(5) are determined. The level scheme of ²¹⁷Ac and the α-decay of N = 128 isotones are discussed.     

Tensor interaction in heavy-ion scattering: (I). The turning-point model

The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power $\text{T}{}_{\mathrm{2q}}$ have certain relations with each other for each type of tensor interaction (T_R, T_P and T_L types). The predicted relations between the $\text{T}{}_{\mathrm{2q}}$ are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for ⁷Li and ²³Na elastic scattering from ⁵⁸Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a T_P? or T_L-type tensor interaction in polarized heavy-ion scattering. The presence of a T_P-type tensor interaction is suggested by measured $\text{T}{}_{20}\text{/}\text{T}{}_{22}$ ratios for ⁷Li+⁵⁸Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail.     

Structural connections between 148Sm and 149Sm nuclei

The ^{146, 148}Nd(α, χn) and ^{148, 150}Nd(³He, χn) reactions at E_α = 20–43 MeV and E_3He = 19–27 MeV, are used to study excited states in the ¹⁴⁹Sm₈₆ and ¹⁴⁹Sm₈₇ nucleides and consequently the low-spin odd-parity excitation. The mixing ratios and multipolarities of the most prominent transitions are deduced from the combined evidence of angular distribution and electron conversion data. The spin-parity assignments for most of the levels observed are established. In ¹⁴⁸Sm the ground state band extending to I^π = 10⁺ is predominantly populated. A negative-parity odd-spin band extending from I^π = 3^?through 11^? is also observed. The bands in ¹⁴⁸Sm are interpreted within the framework of the interacting boson approximation model. In ¹⁴⁹Sm positive-parity levels with spin up to $\text{25}\text{2}$ and negative-parity levels with spins up to $\text{21}\text{2}$ are observed. The predominant γ-decay proceeds via transitions associated with $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$, $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$, $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ intrinsic configurations. The branching ratios B(E1)/B(E2) are calculated and compared in both ¹⁴⁸Sm and ¹⁴⁹Sm nucleides. The B(E1)/B(E2) dependence on the value of Z for some N = 86 (as well as 88 and 84) isotones showing a minimum of Z = 64 was noted. A 4 ns high-spin isomer mainly decaying into the positive-parity band based on the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ state in ¹⁴⁹Sm is found. Experimental evidence is presented to interprete the $\text{1}\text{2}{}^{\mathrm{+}}$, $\text{15}\text{2}{}^{\mathrm{+}}$, … and $\text{9}\text{2}{}^{\mathrm{?}}$, $\text{13}\text{2}{}^{\mathrm{?}}$, …, ΔI = 2, sequences in ¹⁴⁹Sm as arising from the coupling of an $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ neutron to the octupole and quadrupole modes of the ¹⁴⁸Sm core nucleus. The absolute reaction cross sections for the ^{146, 148, 150}Nd(³He, χn) reactions have been determined for different bombarding energies. The mixing of the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ shells is discussed in the framework of an axial-particle-rotor model calculation.     

Systematics of nn states with high spin: A study of the (α, 2He) reaction on fp shell nuclei

At 57 MeV bombarding energy the (α, ²He) reaction has been investigated on targets of ^54,56Fe, ^58,60,62,64Ni, ^64,66Zn, and ⁷⁰Ge. Selective excitation of the 2n configurations $\text{(}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{7?}}$, , and $\text{(}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{6+}}$ was observed in all final nuclei. A linear A and T dependence of the binding energies of these states was observed. This systematic behaviour is well described by the Bansal-French model. The values obtained for the strength of the isoscalar and the isovector parts of the particle-hole interaction are consistent with the average of the values describing the corresponding single-particle states.     

Specific heat of liquid 3He at 29.4 bar

The specific heat of liquid ³He has been measured from 4 to 300 mK. Even at very low temperature, it deviates from a pure γT behavior. The effective mass $\text{m}{}^1\text{= 5.8m}{}_3$ is in good agreement with previous results, but disagrees with recent measurements around T_A.     

Absolute E1, ΔK = 1 transition probabilities between multi-quasiparticle high-spin states in 176Hf and 178Hf

Applying the generalized centroid shift method in (α, 2n) reactions, the half-lives of the 3080 keV 15⁺ state in ¹⁷⁶Hf and of the 1637 keV 5^? state in ¹⁷⁸Hf have been measured as $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.20}{}^{\mathrm{+0.12}}{}_{\mathrm{?0.08}}\text{ns}$ and $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.40 ± 0.10}\text{ns}$, respectively. B(El) values of K-allowed E1 transitions $\text{n}\text{9}\text{2}{}^{\mathrm{+}}\text{[624]→}\text{7}\text{2}{}^{\mathrm{?}}\text{[514]}$ are derived, and together with other data on similar transitions in odd-A nuclei, compared with predictions of the Nilsson plus pairing model. In ¹⁷⁶Hf, the 15⁺ and 14^? states at 3080 and 2866 keV, respectively, appear as quite pure deformed 4QP configurations. In the 2QP state at 1637 keV in ¹⁷⁸Hf, possible strong mixing of vibrational components is discussed coupled via 2QP K-admixtures arising from the partial alignment of the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron.     

The 85Rb(p,d)84Rb reaction

The spectrum seen in single neutron pickup leading to the doubly odd nucleus ⁸⁴Rb is remarkably clean, with only five levels populated by l = 4 and six by l = 1 transitions. A simple 2J+1 weighting for the l = 4 data, combined with previous information on ⁸⁴Rb, allowed the J^π = 2^?–7^? states of the ($\text{v}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^{\mathrm{?3}}\text{? π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^{\mathrm{?3}}$) multiplet to be identified. These data are used to determine the two-hole $\text{π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{-v}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}{}^{\mathrm{?}}$ interaction matrix elements.     

β-delayed charged particles from 9Li and 11Li

β-delayed emission of α-particles from ⁹Li and of both α and ⁶He particles from ¹¹Li is observed. Singles energy spectra and two-dimensional energy spectra of coincident particles are measured. A time-of-flight versus energy measurement is used to identify the mass of the particle. New β-branches are observed which populate high-energy levels in the daughter nuclei. The branching ratios are measured and the β-delayed neutron emission probabilities $\text{P}{}_{\mathrm{<mtext>n</mtext>}}\text{for}{}^9\text{Li and}\text{P}{}_{\mathrm{3n}}\text{for}{}^{11}\text{Li}$ are deduced.     

The particle-hole spectra of 16O and 16N as observed in pick-up reactions from 17O

The reactions ¹⁷O(d, t) ¹⁶O and ¹⁷O(d, τ)¹⁶N have been investigated at E_d = 52 MeV. Energy spectra of tritons and τ-particles have been measured simultaneously up to excitation energies of 22 MeV in ¹⁶O and 10 MeV in ¹⁶N, respectively. Spectroscopic factors have been obtained by a DWBA analysis of the measured angular distributions. From the comparison of the t- and τ-spectra analog (T = 1) states in ¹⁶O could be identified and the distribution of T = 0 and T = 1 spectroscopic strengths could be deduced. Nearly the total $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ hole strengths have been found and the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{and}\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{1}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ particle-hole multiplets could be located both for T = 0 and T = 1. The average residual interactions in both shell-model configurations turned out to be strikingly different.     

Infrared-radio frequency double resonance observations of pure rotational Q-branch transitions of methane

The $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(2)}}$ and $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(1)}}$ transitions of the J = 7 levels of the ground state of CH₄ have been observed by infrared-radio frequency double resonance using the 3.39 μ HeNe laser line. The transition frequencies are 423.02 ± 0.02 MHz and 1246.55 ± 0.02 MHz, respectively. Using these frequencies and the splitting of the E and F₂ levels of the J = 2 state calculated from the molecular beam magnetic resonance spectra of Ozier, the centrifugal distortion constants are derived to be D_t = 132933 ± 10 Hz, H_4t = ? 16.65 ± 0.2 Hz, and H_6t = 10 ± 1 Hz. The J = 15 E⁽¹⁾ → E⁽²⁾ microwave transition is predicted as 14150 ± 9 MHz.     

Lifetimes and g-factors of the 6− and 7− isomers in 66Ga and 68Ga

The 6^? and 7^? isomeric states in ⁶⁶Ga and ⁶⁸Ga at 1440.9 and 1229.6 keV, respectively, have been populated with the (¹³C, 2np) and (¹⁵N, n2p) reactions on natural Fe. The half-lives of these states have been measured to be $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(6}{}^{\mathrm{?}}\text{,}{}^{66}\text{Ga}\text{) = 57.3 ± 1.2}\text{ns}$ and $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(7}{}^{\mathrm{?}}\text{,}{}^{68}\text{Ga}\text{) = 64 ± 2}\text{ns}$. Using previous data on the hyperfine field of Ga in Fe, the g-factors of these states have been determined by means of the TDPAD method. The results are $\text{g(6}{}^{\mathrm{?}}\text{,}{}^{66}\text{Ga}\text{) = 0.129 ± 0.003}$ and $\text{g(7}{}^{\mathrm{?}}\text{,}{}^{68}\text{Ga}\text{) = 0.105 ± 0.003}$. These values are in very good agreement with the independent particle model if one assumes the and configurations and uses the empirical proton and neutron g-factors from odd-A neighboring nuclei instead of the Schmidt values. The large disagreements with experiment when Schmidt values are used show that core polarization effects are important in these nuclei.     

Study of the 58Ni(τ, α)57Ni reaction at 25 MeV

The ⁵⁸Ni(τ, α)⁵⁷Ni reaction has been studied at 25 MeV incident energy. Angular distributions have been measured from 5° to 50° with a split-pole spectrometer up to 13.5 MeV excitation energy. A local zero-range DWBA analysis has been carried out, allowing l-assignments for about eighty levels, most of them previously unknown. An isospin-dependent potential has been used in the calculation of the neutron form factor for both T_<and T_> states, and the C²S values deduced using this procedure are compared to those obtained with the usual separation energy method. Analog states of eleven ⁵⁷Co levels have been identified and the eventuality for isospin mixing in ⁵⁷Ni has been discussed. A sum rule analysis has been carried out and energy centroids of hole states have been determined. About 60% of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{T}{}_{\mathrm{<}}$ strengths and the full $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole strengths are observed. It is shown that the two excess neutrons in the ⁵⁸Ni ground state mainly populate the $\text{2}\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{, 1}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ orbitals, whereas the occupancy number of the $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ subshell is found to be smaller than 0.1%. Some non-pickup angular distributions have also been observed and a CRC analysis assuming two-step processes in the (τ, α) reaction and weak-coupling wave functions for final states has been attempted. Assignments of J^π values are proposed for four ⁵⁷Ni levels, based on this analysis.     

Measurement of the analyzing power of the 3He(d, p)4He reaction below 1 MeV

The analyzing powers iT₁₁, T₂₀, T₂₁ and T₂₂ have been measured for the reaction ³He(d, p)⁴He at laboratory energies of 344, 465 and 727 keV. A polarized deuteron beam was used with quantization axis oriented perpendicular to and at 54.7° to the incident beam direction. With semi-conductor proton detectors in two perpendicular planes all four analyzing powers could be determined. The beam polarization was determined using the ³H(d, n)⁴He reaction at a mean energy of 130 keV. The uncertainty in this analyzing power and the effect on the results is discussed. The analyzing powers have been fitted to a Legendre polynomial expansion to four or five terms and the resulting coefficients tabulated. The results indicate that d-waves contribute to the reaction only through the ${}^4\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ entrance channel and their contribution falls off both above and below the $\text{3}\text{2}{}^{\mathrm{+}}$ resonance at 430 keV.     

Shell-model studies of the 90Y, 91Zr, 92Nb and 93Mo nuclei

A shell-model calculation of the N = 51, 39 ≦ Z ≦ 42 nuclei is presented. The ⁸⁸Sr nucleus is assumed to be an inert closed core. The extra-core protons are restricted to the ($\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{1}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$) configurations, and the active neutron is allowed to occupy the $\text{2}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{3}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{2}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{1}\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbits. The proton-proton effective interaction is directly taken from the previous analysis on the energy levels for N = 50 isotones by Ball et al. The proton-neutron effective interaction is assumed to be of the form of the surface δ-interaction. The energy spectra are calculated from a least-squares fit to the experimental data, varying the T = 0 and T = 1 strengths of the surface δ-interaction. Spectroscopic factors, E2 transition rates and two-body matrix elements are also calculated and compared with the observed values and the previous theoretical results.     

Critical slowing down of fluctuations in squaric acid (H2C4O4) at the phase transition observed by 13C spin-lattice relaxation

Spin lattice relaxation T₁ of naturally abundant ¹³C nuclei in squaric acid was measured close to the antiferroelectric-paraelectric phase transition temperature T_c = 373 K. A rapid increase in $\text{1}\text{T}{}_1$ is observed close to T_c coming from above, which follows the power law $\text{1}\text{T}{}_1\text{～ ε}{}^{\mathrm{?1.4}}$ where $\text{ε =}\text{(T ? T}{}_{\mathrm{c}}\text{)}\text{T}{}_{\mathrm{c}}$. This behaviour is explained on the basis of the two-dimensional character of the fluctuations.