Bombarding energy dependence of angular momentum transfer in deep inelastic collisions

Measurements of first and second moments of γ-ray multiplicity distributions from deep inelastic collisions of ⁸⁶Kr + ¹⁵⁴Sm are reported. A global systematics of the angular momentum distributions from deep inelastic reactions with projectile masses ? 40 is presented. The average angular momentum is found to depend linearly on the incident channel average angular momentum, while no simple systematics for the second moment appears obvious. In order to illuminate the question whether the angular momentum transfer process reaches statistical equilibrium in deep inelastic collisions, numerical calculations have been performed on two models: a two-sphere classical model including the collective modes of twisting, bending, wriggling and tilting, and a statistical equilibrium Fermi-gas model. The two-sphere classical model is not able to account for the observed second moments, and neither does the Fermi-gas model give an explanation of the deep inelastic multiplicity data.     

Effects of particle evaporation on the angular momentum of the emitting nucleus for deep inelastic and compound nuclear reactions

A model is developed which allows one to calculate analytically the angular momentum removed, and the angular momentum misalignment created by the evaporation of light particles from an excited nucleus. The mass, temperature and angular momentum of the emitting nucleus are explicitly considered. The formalism applies equally well to heavy-ion and compound nuclear reactions.     

Study of continuum gamma rays following low angular momentum reactions

The continuum γ-rays following the reaction ¹⁶⁶Er(α, 2n)¹⁶⁸Yb have been studied at bombarding energies of 21, 27 and 36 MeV. The shape of the statistical γ-rays below 1 MeV was deduced. A low energy bump at ～300 keV was observed. This may arise from transitions along bands at and above the pairing gap.     

Angular momentum fluctuation energy in the cranking model

Angular momentum is approximately projected from Hartree-Fock-Bogoliubov cranked (HFBC) wave functions. At each J the projected energy is $\text{E}{}_{\mathrm{<mtext>proj</mtext>}}\text{≈ E}{}_{\mathrm{<mtext>HFBC</mtext>}}\text{? (Δ}\text{J}\text{)}{}^2\text{/2}\text{J}{}_{\mathrm{<mtext>HFBC</mtext>}}$. The spin-dependent fluctuation $\text{Δ}\text{J}$ includes contributions from J_y and J_z as well as J_x. There are no correlations in the three angular momentum components. Projected energies are calculated for ^{168, 170}Yb and ¹⁷⁴Hf. When compared to experimental energies, the projected spectra are less compressed than the HFBC spectra. At low spins the projected and experimental energies are in good agreement.     

Resonance neutron capture gamma rays in 177Hf

Primary capture γ-rays have been studied for 38 ¹⁷⁷Hf neutron resonances with energies in the range 1–165 eV. Intensities were measured for 29 transitions ending at states with an excitation energy in ¹⁷⁸Hf up to 2050 keV. The analysis was facilitated by the previous knowledge of the spin and parity of all neutron resonances and of most low-lying states. For nine final levels, which had not previously been seen, information on J and π was deduced from the corresponding average intensities. The distribution of partial widths was fitted with a χ² function with ν = 1.38_?0.13^+0.18 degrees of freedom for E1 radiation and ν = 1.5_?0.40^+0.60 for M1 radiation. The average El reduced photon strength was found to be $\text{S}{}_{\mathrm{<mtext>El</mtext>}}\text{= 〈Γ}{}_{\mathrm{\gamma itij}}\text{/DE}{}_{\mathrm{\gamma }}{}^5\text{〉A}{}^{\mathrm{<mtext>?8</mtext><mtext>3</mtext>}}\text{= (4.8 ± 1.0) × 10}{}^{\mathrm{?15}}\text{MeV}{}^{\mathrm{?5}}$ and the ratio between El and Ml intensities equal to 5.5 ± 1.4. A comparison of this value for the El strength with those reported for other nuclei with A$\text{\$}\text{?}$= 100 showed that the intensities follow the A-dependence predicted by the Brink-Axel model. A non-statistical effect was observed, consisting of an enhancement of El transition probalilities to K = 2, 3 final states as compared to K = 0, 4 states.     

Q- and Z-dependence of angular momentum transfer in deeply inelastic collisions of 86Kr with 209Bi

The dependence of the in-plane and out-of-plane angular correlations of fragments from fissioning heavy products on the kinetic energy and Z of the light reaction partner have been measured. From the dependence of the angular correlations on Q-value and hence energy loss, together with existing data from which the total angle-integrated cross section as a function of energy loss can be extracted, we have determined the dependence of the angular momentum transferred to the heavy product on the initial orbital angular momentum or impact parameter. The resulting dependence is qualitatively consistent with the sticking limit for a reaction intermediate of touching deformed fragments. More specific nuclear models generally underestimate the angular momentum transfer, although the one-body proximity-friction model accounts for the major fraction of the angular momentum transfer. A recent model incorporating both one-body proximity friction and collective excitations accounts quite well for the observed angular momentum transfer. The Z-dependendence of the anisotropy shows the importance of angular momentum fractionation for the less probable events, where the Z of the fissioning system is appreciably less than that of the target. The transferred angular momentum is shown to be fairly strongly aligned along the perpendicular to the reaction plane, with alignment values of 0.6 to 0.8. The component of angular momentum not along the perpendicular to the reaction plane is found to be primarily oriented perpendicular rather than parallel to the recoil direction. The absolute fission probabilities are found to be qualitatively consistent with J-dependent calculations using the J-values deduced from the angular correlations.     

The elastic and inelastic scattering of intermediate energy protons on deuterium at small momentum transfer

The differential cross sections for the elastic and inelastic scattering of protons on deuterium have been measured for scattering angles less than 14° at 198.5, 297.6 and 456.6 MeV. These quantities were determined relative to dσ / dΩ for pp elastic scattering with a precision of typically 2%. The range of excitation energies for the (p, p') reaction was chosen to emphasize the region near the np threshold dominated by the final-state interaction in the ¹S₀ channel. Particular attention was given to the dependence on excitation energy of the spectra at 198.5 MeV to examine the sensitivity to the ¹S₀ scattering length, a_np In this paper all data are compared with a new, detailed formulation of a simple model of the reaction mechanism based on the impulse approximation. The experimental results differ from the predictions by typically 10% and the differential cross sections exhibit a sensitivity to the intermediate-energy nucleon-nucleon amplitudes. If the impulse approximation is used to estimate a_np from the data at 198.5 MeV a value of − 24.7 ± 0.4 fm is obtained.     

High momentum transfer approach to inelastic electron scattering on nuclei and model-independent description of nuclear transition densities

A method of approximating the DWBA transition amplitude at higher momentum transfers is given. It leads to quantitative agreement with the DWBA values, combined with a considerable saving of computing time. The method permits model-independent analyses of inelastic data at higher momentum transfers. The influence of uncertainties in the ground state charge density on the inelastic cross section is studied and found to be negligible. Regardless of the magnitude of Coulomb distortions, the multipole moments B(τ; L, q) are shown to be model-independent quantities for those values of q which lie in the region of measured momentum transfers.     

A study of γ-decay modes from high angular momentum nuclear states by high order multiplicity measurements

Reactions between ¹⁸O and ¹⁶O ions, with energies well above the Coulomb barrier, and ^{148, 150}Nd target nuclei were used to study the cascades of γ-rays in the residual nuclei ^{161, 162}Er. A multi-counter setup was used in which the γ-rays were detected by a Ge(Li) counter coupled in coincidence with up to 9 NaI(Tl) counters. The γ-multiplicity has been studied for γ-rays cascading through states above and along the yrast line. Higher moments of the multiplicity distributions (shape parameters) were deduced from the data. These moments allow the construction of the spin distribution for the entry states. The difference between these spin distributions from reactions induced by ¹⁶O and ¹⁸O ions was studied. Also the fusion cross section was measured for the two systems as a function of bombarding energy and compared to the multiplicity results at two different excitation energies (E_x = 49.5 and 56.2 MeV). A subtraction technique has been applied in the data analysis with the intention to study the decay of a selected part of the high-spin region, and the results show besides the 4n channel an unexpected large contribution of the 5n channel from this region. The sidefeeding patterns of the multiplicity distributions are extracted and show a significant difference for the ¹⁶O and ¹⁸O induced reactions, especially at the lowest bombarding energies. The results are compared with statistical model calculations.     

Gamma ray multiplicities in deep inelastic collisions for the Cu + Au 400 MeV system

For the Cu + Au 400 MeV system γ-ray multiplicities have been measured. The mean value of the transferred angular momentum, the variances, and the repartition of angular momentum between the fragments have been deduced. It is shown that, early in the reaction the building up of angular momentum is a very fast process. For longer times, additional angular momentum is induced in the fragments. The excitation of collective modes can account for this effect. The properties of such modes have been analysed.     

Emission of α-particles in deep inelastic reactions induced by 148 MeV 14N

Energy and angular correlations between α-particles and heavy ejectiles have been measured for 148 MeV ¹⁴N incident on ¹²C, ²⁷Al and ⁵⁸Ni targets. The coincidence cross sections for ejectiles with Z < 6 may be parametrised as a product of singles cross sections for the detection of α-particles and heavy ions. For ²⁷Al and ⁵⁸Ni targets, this indicates that the α-particles are emitted at an early stage of the reaction prior to the formation of the deep inelastic fragments. For the ¹²C target, however, kinematic effects are found to dominate the observed correlations. For $\text{Z ≧ 6}$ ejectiles the observed correlations appear consistent with the emission of α-particles from the recoiling nucleus produed in the reaction.     

Energy and angular momentum transfers in equilibrium and pre-equilibrium 158Gd(α, xn) reactions

Neutron time-of-flight spectra and γ-ray multiplicities were measured in coincidence with discrete γ-rays for specific exit channels in the ¹⁵⁸Gd(α, xn) reactions at E_α = 70 MeV. The neutron energy spectra and angular distributions were analysed in terms of equilibrium and non-equilibrium decay processes. Significant emission of non-equilibrated neutrons was found, amounting to about 40 %, 25 % and 15 % of the total neutron emission in the 4n, 5n and 6n exit channels, respectively. The corresponding average kinetic energies in this precompound phase were around 12, 8 and 4.5 MeV. The angular momentum carried away by the neutrons was found to be rather constant for all exit channels and on the average about 3? units. It is found that the total energy and angular momentum removed by the neutrons and γ-rays agrees within the experimental errors with the calculated values for the compound nucleus.     

Angular momentum transfer in 12C-, 20Ne- and 40Ar-induced fission

Angular momentum transfer in a variety of ¹²C-, ²⁰Ne- and ⁴⁰Ar-induced fission reactions has been investigated using γ-ray multiplicity techniques. Fission fragments were detected in coincidence using a pair of solid-state detectors. The fragment masses were deduced from the kinetic energies and emission angles using two-body kinematics. The γ-ray multiplicities (M_γ) of the fission fragments were measured utilizing an array of eight NaI detectors. For most of the systems studied, M_γ is nearly independent of the exit-channel mass asymmetry. The strongest dependence on mass is observed in the systems ¹⁵⁴sm + 240 MeV ⁴⁰Ar, where a minimum exists at symmetry, and ¹⁹⁷Au + 164 MeV ²⁰Ne, where nuclear structure effects are suggested by the data. For all the reactions the quantity M_γ tends to decrease gradually with increasing fragment kinetic energy. The magnitude of M_γ generally appears to be larger than expected on the basis of rigid rotation, suggesting a spin enhancement effect. The data are compared with a simple model which assumes the statistical excitation of a variety of angular momentum bearing collective modes. Reasonable agreement is obtained with the experimental results. The roles of other collective effects, such as shape fluctuations and angular momentum fractionation, are also considered.     

Total cross-section measurements for the production of nuclear gamma rays from light nuclei by low-energy deuterons

The thick target yields of the reactions ⁶Li, ⁹Be, ¹⁰B(d, nγ) for specific final nucleus γ-rays have been measured between deuteron bombarding energies of 48 and 170 keV. The measured thick target yields are used, together with recently published values of the stopping power of low-energy deuterons in matter, to infer the total reaction cross sections for the production of the specific γ-rays between deuteron energies of 65 and 160 keV. The cross sections are compared to appropriate Coulomb barrier penetration probabilities and the astrophysical functions S(E) are deduced.     

Binary aspects and particle multiplicities of the fragments from natAg+340 MeV 40Ar deep inelastic collisions

Deep inelastic fragments from the reaction ^natAg+340 MeV ⁴⁰Ar have been studied in coincidence. Charged particles (10 ≦ Z ≦ 32) were detected and identified in Z by means of a ΔE?E telescope, while the complementary fragments were detected in a one-dimensional, solid-state position-sensitive detector. Both in-plane and out-of-plane correlations were measured. The results confirm the binary nature of the deep inelastic process for this reaction. From the measured energies and angles of the fragments and the atomic number of one of the fragments, it was possible to determine the total mass loss due to the de-excitation of the fragments as well as the total evaporated charge at symmetry. An iterative procedure is discussed which enables one to determine the masses and kinetic energies of the fragments before evaporation, as well as the total number of particles evaporated by each fragment. The widths of the in-plane and out-of-plane correlations agree with the results of the iterative calculations, as do evaporation calculations which are based on the charge equilibrium model. The experimental results support the charge equilibrium model and indicate that thermal equilibrium is achieved between the fragments at fixed mass asymmetry.     

Measurement of a 4π angular pattern for α-decay of 12C excited by inelastic deuteron scattering

The reaction ¹²C(d, d′)¹²C(3^?,9.6MeV) → α + ⁸Be(g.s.), was studied experimentally at 26 MeV deuteron energy with the multi-detector system BOL. The grid of angular coordinates at which data were taken is evenly spread over the available phase space. The angular correlation function of the inelastically scattered deuteron and the α-particle emitted by the excited ¹²C nucleus was obtained. Experimental results are presented as the coefficients of an expansion in spherical harmonics. A DWBA analysis can explain the measured angular correlation pattern in a qualitative way only.     

Elastic and inelastic scattering of 17.5 and 40.0 MeV 3He particles from 11B

The ³He scattering cross sections have been measured at 17.5 and 40.0 MeV from the ground state and first four excited levels of ¹¹B. The results are analysed with the SCA assuming ¹¹B to be a symmetric rotator and including the K-band mixing introduced by the Coriolis force. A systematic attempt is made to deduce the hexadecapole moment and the sign of the quadrupole deformation of ¹¹B.     

Angular and energy dependences of emission probability for light particles in 22Ne-induced reactions at 8 MeV/nucleon

Inclusive energy spectra and angular distributions have been measured for light charged particles with Z = 1–4 emitted in the interaction of ²²Ne ions with a ¹⁸¹Ta target. The reaction products were analysed and detected by means of a system of ΔE-E telescopes placed in the focal plane of a magnetic spectrometer. The end-point energies of the light particles correspond to the calculated kinematic limits taking into account the rotational energy of the residual nucleus. The angular distributions of the high-energy particles are strongly forward peaked. The data obtained are analysed on the basis of the moving source, rotating hot spot, massive transfer and breakup fusion models. The relative yields of the different isotopes and their most probable energies are described by the massive transfer model. The qualitative behaviour of the spectra in the vicinity of the kinematic limits can be explained in terms of the breakup fusion model.     

Multiplicity and angular distributions of charged particles in interactions of Fe in emulsion at 2.5A GeV/c

Data are presented on multiplicity and angular distributions of charged secondary particles from inelastic interactions of ⁵⁶Fe in emulsion at 2.5A GeV/c. Comparisons with data, at nearby the same incident momentum per nucleon from p-A, ¹⁴N-A, ¹⁶O-A and ⁴⁰Ar-A collisions are performed in order to trace the dependence on projectile and target mass. Furthermore, the ⁵⁶Fe data are compared with the results from a cascade-evaporation model. This comparison shows some significant deviations between the model and the data which are not observed for light ion induced collisions.