Brian W Bush

Y. Alhassid and B. Bush, “Stochastic approach to giant dipole resonances in hot rotating nuclei,” Phys. Rev. Lett., vol. 63, no. 22, pp. 2452–2455. <http://link.aps.org/doi/10.1103/PhysRevLett.63.2452>
A stochastic macroscopic approach to giant dipole resonances (GDR’s) in hot rotating nuclei is presented. In the adiabatic limit the theory reduces exactly to a previous adiabatic model where the unitary invariant metric is used to calculate equilibrium averages. Nonadiabatic effects cause changes in the GDR cross section and motional narrowing. Comparisons with experiments where deviations from the adiabatic limit are substantial are shown and can be used to determine the damping of the quadrupole motion at finite temperature.

Y. Alhassid and B. Bush, “Effects of thermal fluctuations on giant dipole resonances in hot rotating nuclei,” Nuclear Physics A, vol. 509, no. 3, pp. 461–498. <http://www.sciencedirect.com/science/article/pii/0375947490900873>
We present a macroscopic approach to giant dipole resonance (GDR) in highly excited nuclei, using a unified description of quadrupole shape thermal fluctuations. With only two free parameters, which are fixed by the zero-temperature nuclear properties, the-model reproduces well experimental GDR cross sections in the 100 ≤ A ≤ 170 mass range for both spherical and deformed nuclei. We also investigate the cross-section systematics as a function of both temperature and angular velocity and the sensitivity of the GDR peak to the nuclear shape. We conclude that at low temperatures (T ≈ 1 MeVfs) the GDR cross section is sensitive to changes in the nuclear energy surface. Higher-temperature (T ≳ 2 MeV) cross sections are dominated by large fluctuations (triaxial in particular) and are much less sensitive to the equilibrium shape.

Y. Alhassid and B. Bush, “Orientation fluctuations and the angular distribution of the giant-dipole-resonance γ rays in hot rotating nuclei,” Phys. Rev. Lett., vol. 65, no. 20, pp. 2527–2530. <http://link.aps.org/doi/10.1103/PhysRevLett.65.2527>
A recent macroscopic approach to the giant dipole resonances in hot rotating nuclei is extended to include the angular distributions of the γ rays emitted in the resonance decay. It provides a uniform description of thermal fluctuations in all quadrupole shape degrees of freedom within the framework of the Landau theory. In particular, the inclusion of fluctuations in the nuclear orientation with respect to the rotation axis is crucial in reproducing the observed attenuation of the angular anisotropy. The theory is applied to recent precision measurements in 90Zr and 92Mo and is the first to reproduce well both the observed giant-dipole-resonance cross sections and the angular anisotropies.

Y. Alhassid and B. Bush, “Time-dependent shape fluctuations and the giant dipole resonance in hot nuclei: Realistic calculations,” Nuclear Physics A, vol. 514, no. 3, pp. 434–460. <http://www.sciencedirect.com/science/article/pii/037594749090151B>
The effects of time-dependent shape fluctuations on the giant dipole resonance (GDR) in hot rotating nuclei are investigated. Using the framework of the Landau theory of shape transitions we develop a realistic macroscopic stochastic model to describe the quadrupole time-dependent shape fluctuations and their coupling to the dipole degrees of freedom. In the adiabatic limit the theory reduces to a previous adiabatic theory of static fluctuations in which the GDR cross section is calculated by averaging over the equilibrium distribution with the unitary invariant metric. Nonadiabatic effects are investigated in this model and found to cause structural changes in the resonance cross section and motional narrowing. Comparisons with experimental data are made and deviations from the adiabatic calculations can be explained. In these cases it is possible to determine from the data the damping of the quadrupole motion at finite temperature.

Y. Alhassid and B. Bush, “Time-dependent fluctuations and the giant dipole resonance in hot nuclei: Solvable models,” Nuclear Physics A, vol. 531, no. 1, pp. 1–26. <http://www.sciencedirect.com/science/article/pii/037594749190565N>
A recent macroscopic theory of time-dependent shape fluctuations in hot nuclei and their effects on the giant dipole resonance is investigated in the context of solvable models with one quadrupole shape degree of freedom. Using the framework of the Landau theory of shape transitions, both the quadrupole shape and the giant dipole degrees of freedom are described by a coupled set of stochastic equations. Two solvable models for which the dipole correlation function is found in closed form are discussed; one for a spherical nucleus and one for a deformed nucleus. The adiabatic and sudden limits of the models are examined. The latter limit is shown to produce a phenomenon known as motional narrowing. For the more general cases we introduce Monte Carlo techniques and test them against the solvable models.

Y. Alhassid and B. Bush, “Effects of orientation fluctuations on the angular distribution of the giant dipole resonance γ-rays in hot rotating nuclei,” Nuclear Physics A, vol. 531, no. 1, pp. 39–62. <http://www.sciencedirect.com/science/article/pii/037594749190567P>
The macroscopic approach to the GDR in hot rotating nuclei is extended to include the angular distribution of the emitted GDR γ-rays. The effects of thermal shape fluctuation and in particular fluctuations in the nuclear orientation with respect to the rotation axis, are discussed in the framework of the Landau theory. It is found that while orientation fluctuations have negligible effects on the GDR cross section, they cause significant attenuation in the angular anisotropy parameter a2 which offsets the a2 enhancement due to intrinsic shape fluctuations. It is shown that this fluctuation theory is successful in reproducing both the observed cross section and a2 in highly excited 90Zr and 92Mo compound nuclei. The non-adiabatic effects on a2 are studied in terms of a time-dependent model for the quadrupole shape fluctuations.

Y. Alhassid and B. Bush, “The systematics of the Landau theory of hot rotating nuclei,” Nuclear Physics A, vol. 549, no. 1, pp. 12–42. <http://www.sciencedirect.com/science/article/pii/037594749290065R>
The Landau theory of hot rotating nuclei, which was recently introduced to explain the universal features of the shape transitions, is shown to describe well many nuclei at moderate temperatures (T ≳ 1 MeV) and spin. The Landau parameters are extracted from microscopic calculations. Their systematics as a function of temperature and neutron numbers is demonstrated for the neodynium isotopes with even number of neutrons. An extended Landau theory is introduced to describe better nuclei at lower temperatures and /or higher spins.

Y. Alhassid and B. Bush, “Nuclear level densities in the static-path approximation: (I). A solvable model,” Nuclear Physics A, vol. 549, no. 1, pp. 43–58. <http://www.sciencedirect.com/science/article/pii/037594749290066S>
We investigate the static-path approximation (SPA) and mean-field approximation (MFA) for the level density within a solvable SU(2) model. Comparing the SPA level density to the MFA one, we find an enhancement with a great sensitivity to the interaction strength, in agreement with exact analytic results. This enhancement compensates for a corresponding suppression which occurs at negative temperatures. The saddle-point approximation used in converting the partition function to the level density works well at all but low energies.

Y. Alhassid and B. Bush, “Nuclear level densities in the static-path approximation: (II). Spin dependence,” Nuclear Physics A, vol. 565, no. 2, pp. 399–426. <http://www.sciencedirect.com/science/article/pii/037594749390218M>
The static-path approximation (SPA) and mean-field approximation (MFA) for the partition function and level density are investigated with the inclusion of spin. The methods are studied within a solvable model, the nuclear SU(3) Elliot model. The SPA partition function is enhanced compared with the MFA partition function and is in good agreement with the exact result at all angular velocities (or spins) and at all but low temperatures. The error made in the SPA as well as in the saddle-point approximation used in the conversion from angular velocity to spin is only weakly dependent on the spin and is small at not too low temperatures (or excitation energies).

Y. Alhassid, B. Bush, and S. Levit, “Landau theory of shapes, shape fluctuations and giant dipole resonances in hot nuclei,” Nuclear Physics A, vol. 482, no. 1–2, pp. 57–64. <http://www.sciencedirect.com/science/article/pii/0375947488905751>
Universal features of evolution of the equilibrium nuclear shapes with temperature and angular momentum are predicted by the Landau theory of nuclear shape transitions. The general dependence of the nuclear free energy on the deformation given by this theory also provides a unified description of thermal fluctuations of all quadrupole degrees of freedom. Using this unified theory we calculate the giant dipole absorption by hot rotating nuclei and investigate its systematics as a function of nuclear spin and temperature. Direct comparison with experimental data is presented.

Y. Alhassid, B. Bush, and S. Levit, “Thermal Shape Fluctuations, Landau Theory, and Giant Dipole Resonances in Hot Rotating Nuclei,” Phys. Rev. Lett., vol. 61, no. 17, pp. 1926–1929. <http://link.aps.org/doi/10.1103/PhysRevLett.61.1926>
A macroscopic approach to giant dipole resonances (GDR’s) in hot rotating nuclei is presented. It is based on the Landau theory of nuclear shape transitions and provides a unified description of thermal fluctuations in all quadrupole shape degrees of freedom. With all parameters fixed by the zero-temperature nuclear properties the theory shows a very good agreement with existing GDR measurements in hot nuclei. The sensitivity of the GDR peak to the shape of hot nuclei is critically examined. Low-temperature experimental results in Er show clear evidence for changes in the nuclear energy surface, while higher-temperature results are dominated by the fluctuations.

B. Bush and Y. Alhassid, “On the width of the giant dipole resonance in deformed nuclei,” Nuclear Physics A, vol. 531, no. 1, pp. 27–38. <http://www.sciencedirect.com/science/article/pii/037594749190566O>
Applying surface dissipation models to the Goldhaber-Teller model, we calculate the dependence of the giant dipole resonance (GDR) width on the nuclear quadrupole deformation. When expressed in units of the spherical width, this width reduces to a purely geometrical elliptic integral. It is shown to be very well approximated by the empirical power law with an exponent of 1.6. This approach utilizes no free parameters and reproduces the experimentally observed width dependence for GDR’s built on the ground state of heavy nuclei. The formula derived here plays an important role in a recently developed macroscopic approach to the GDR in hot rotating nuclei.

B. Bush and J. Nix, “Classical Hadrodynamics: Foundations of the Theory,” Annals of Physics, vol. 227, no. 1, pp. 97–150. <http://www.sciencedirect.com/science/article/pii/S0003491683710778>
We derive and discuss the classical relativistic equations of motion for an action corresponding to extended nucleons interacting with massive, neutral scalar and vector meson fields. This theory, which we call classical hadrodynamics, is the classical analogue of the quantum hadrodynamics of Serot and Walecka but without the assumptions of the mean-field approximation and of point nucleons. The theory is manifestly covariant and allows for non-equilibrium phenomena, interactions among all nucleons, and meson production when used for applications such as relativistic heavy-ion collisions. We review the history of classical meson field theory, with special emphasis on issues related to self-interaction, preacceleration, runaway solutions, and finite-size effects. Sample calculations are presented for nucleon-nucleon collisions at plab = 200 GeV/c, where we find that the theory provides a physically reasonable description of gross features assaciated with the dominating soft reactions. The equations of motion are practical to solve numerically for ultrarelativistic heavy-ion collisions.

B. W. Bush and J. Nix, “Classical hadrodynamics: application to soft nucleon-nucleon collisions,” Nuclear Physics A, vol. 560, no. 1, pp. 586–602. <http://www.sciencedirect.com/science/article/pii/037594749390116F>
We present results for soft nucleon-nucleon collisions at Plab = 14.6, 30, 60, 100 and 200 GeV/c calculated on the basis of classical hadrodynamics for extended nucleons. This theory, which corresponds to nucleons of finite size interacting with massive neutral scalar and vector meson fields, is the classical analogue of the quantum hadrodynamics of Serot and Walecka but without the assumptions of the mean-field approximation and of point nucleons. The theory is manifestly Lorentz-covariant and automatically includes space-time nonlocality and retardation, nonequilibrium phenomena, interactions among all nucleons and particle production when used for applications such as relativistic heavy-ion collisions. We briefly review the history of classical meson-field theory and present our classical relativistic equations of motion, which are solved to yield such physically observable quantities as scattering angle, transverse momentum, radiated energy and rapidity. We find that the theory provides a physically reasonable description of gross features associated with the soft reactions that dominate nucleon-nucleon collisions. The equations of motion are practical to solve numerically for relativistic heavy-ion collisions.

B. W. Bush and J. Nix, “Classical hadrodynamics: A new approach to ultrarelativistic heavy-ion collisions,” Nuclear Physics A, vol. 583, no. 0, pp. 705–710. <http://www.sciencedirect.com/science/article/pii/037594749400748C>
We discuss a new approach to ultrarelativistic heavy-ion collisions based on classical hadrodynamics for extended nucleons, corresponding to nucleons of finite size interacting with massive meson fields. This new theory provides a natural covariant microscopic approach that includes automatically spacetime nonlocality and retardation, nonequilibrium phenomena, interactions among all nucleons and particle production. In the current version of our theory, we consider N extended unexcited nucleons interacting with massive neutral scalar (σ) and neutral vector (ω) meson fields. The resulting classical relativistic many-body equations of motion are solved numerically without further approximation for soft nucleon-nucleon collisions at plab = 14.6, 30, 60, 100 and 200 GeV/c to yield the transverse momentum imparted to the nucleons. For the future development of the theory, the isovector pseudoscalar (π+, π−, π0), isovector scalar (δ+, δ−, δ0), isovector vector (ϱ+, ϱ−, ϱ0) and neutral pseudoscalar (η) meson fields that are known to be important from nucleon-nucleon scattering experiments should be incorporated. In addition, the effects of quantum uncertainty on the equations of motion should be included by use of techniques analogous to those used by Moniz and Sharp for nonrelativistic quantum electrodynamics.

B. W. Bush and J. R. Nix, “New Approach to the Interaction of Cosmic Rays with Nuclei in Spacecraft Shielding and the Human Body,” Los Alamos National Laboratory, Report LA-12452-MS.
The interaction of high-energy cosmic rays with nuclei in spacecraft shielding and the human body is important for manned interplanetary missions and is not well understood either experimentally or theoretically. We present a new theoretical approach to this problem based on classical hadrodynamics for extended nucleons, which treats nucleons of finite size interacting with massive meson fields. This theory represents the classical analogue of the quantum hadrodynamics of Serot and Walecka without the assumptions of the mean-field approximation and point nucleons. It provides a natural covariant microscopic approach to collisions between cosmic rays and nuclei that automatically includes space-time non-locality and retardation, nonequilibrium phenomena, interactions among all nucleons, and particle production. Unlike previous models, this approach is manifestly Lorentz covariant and satisfies a priori the basic conditions that are present when cosmic rays collide with nuclei, namely an interaction time that is extremely short and a nucleon mean-free path, force range, and internucleon separation that are all comparable in size. We review the history of classical meson-field theory and derive the classical relativistic equations of motion for nucleons of finite size interacting with massive scalar and vector meson fields.

B. W. Bush and J. R. Nix, “Classical hadrodynamics for extended nucleons,” in Proc. 8th Winter Workshop on Nuclear Dynamics, Jackson Hole, Wyoming, p. 311–316. <http://www.osti.gov/energycitations/servlets/purl/5692537-Wl0CTO/>
We discuss a new approach to relativistic nucleus-nucleus collisions based on classical hadrodynamics for extended nucleons, corresponding to nucleons of finite size interacting with massive meson fields. This theory provides a natural covariant microscopic approach to relativistic nucleus-nucleus collisions that includes automatically spacetime nonlocality and retardation, nonequilibrium phenomena, interactions among all nucleons, and particle production. Inclusion of the finite nucleon size cures the difficulties with preacceleration and runaway solutions that have plagued the classical theory of self-interacting point particles.

B. W. Bush and J. R. Nix, “Particle-production mechanism in relativistic heavy-ion collisions,” in Proc. 7th Int. Conf. on Nuclear Reaction Mechanism, Varenna, Italy, p. 592. <http://www.osti.gov/energycitations/servlets/purl/10162609-gv1Z8s/native/>
We discuss the production of particles in relativistic heavy-ion collisions through the mechanism of massive bremsstrahlung, in which massive mesons are emitted during rapid nucleon acceleration. This mechanism is described within the framework of classical hadrodynamics for extended nucleons, corresponding to nucleons of finite size interacting with massive meson fields. This new theory provides a natural covariant microscopic approach to relativistic heavy-ion collisions that includes automatically spacetime nonlocality and retardation, nonequilibrium phenomena, interactions among all nucleons, and particle production. Inclusion of the finite nucleon size cures the difficulties with preacceleration and runaway solutions that have plagued the classical theory of self-interacting point particles. For the soft reactions that dominate nucleon-nucleon collisions, a significant fraction of the incident center-of-mass energy is radiated through massive bremsstrahlung. In the present version of the theory, this radiated energy is in the form of neutral scalar (σ) and neutral vector (ω) mesons, which subsequently decay primarily into pions with some photons also. Additional meson fields that are known to be important from nucleon-nucleon scattering experiments should be incorporated in the future, in which case the radiated energy would also contain isovector pseudoscalar (π+, π–, π0), isovector scalar (δ+, δ–, δ0), isovector vector (ρ+, ρ–, ρ0), and neutral pseudoscalar (η) mesons.

B. W. Bush, G. F. Bertsch, and B. A. Brown, “Shape diffusion in the shell model,” Phys. Rev. C, vol. 45, no. 4, pp. 1709–1719. <http://link.aps.org/doi/10.1103/PhysRevC.45.1709>
The diffusion coefficient for quadrupolar shape changes is derived in a model based on the mixing of static Hartree-Fock configurations by the residual interaction. The model correctly predicts the width of single-particle configurations. We find a diffusion rate depending on temperature as T3, consistent with at least one other theoretical estimate. However, our diffusion rate is an order of magnitude lower than two values extracted from data.

B. W. Bush, J. R. Nix, and A. J. Sierk, “Spacetime nonlocality and retardation in relativistic heavy-ion collisions,” in Presented at the 7th Winter Workshop on Nuclear Dynamics, Key West, 27 Jan. - 2 Feb. 1991, Key West, Florida, vols. -1, p. 282–287. <http://adsabs.harvard.edu/abs/1991nudy.workR….B>
We discuss the exact numerical solution of the classical relativistic equations of motion for a Lagrangian corresponding to point nucleons interacting with massive scalar and vector meson fields. The equations of motion contain both external retarded Lorentz forces and radiation-reaction forces; the latter involve nonlocal terms that depend upon the past history of the nucleon in addition to terms analogous to those of classical electrodynamics. The resulting microscopic many-body approach to relativistic heavy-ion collisions is manifestly Lorentz covariant and allows for nonequilibrium phenomena, interactions with correlated clusters of nucleons, and particle production. For point nucleons, the asymptotic behavior of nucleonic motion prior to the collision is exponential, with a range in proper time of approximately 0.5 fm. However, this behavior is altered by the finite nucleon size, whose effect we are currently incorporating into our equations of motion. The spacetime nonlocality and retardation that will be present in the solutions of these equations may be responsible for significant collective effects in relativistic heavy-ion collisions.

B. W. Bush, J. R. Nix, and A. J. Sierk, “Classical hadrodynamics approach to ultrarelativistic heavy‐ion collisions,” in AIP Conference Proceedings, Tucson, Arizona, vol. 243, pp. 835–837. <http://proceedings.aip.org/resource/2/apcpcs/243/1/835_1?isAuthorized=no>
We discuss the exact solution of the classical relativistic equations of motion for an action corresponding to nucleons interacting with massive scalar and vector meson fields. This model−the classical analogue of the quantum hadrodynamics of Serot and Walecka−provides a manifestly Lorentz covariant approach to heavy‐ion collisions, allows for nonequilibrium phenomena, interactions of correlated nucleon clusters, and particle production, and is valid when interaction times are short. We present an analysis of the nonlocality inherent in the model and discuss effects arising from the finite size of a nucleon.

Bush, B.W. and Nix, J.R., “Calculations of Ultrarelativistic Nucleus-Nucleus Collisions Based on Classical Hadrodynamics for Extended Nucleons,” in Contributed Papers and Abstracts, Quark Matter ’91, Ninth Int. Conf. on Ultra-Relativistic Nucleus-Nucleus Collisions, Gatlinburg, Tennessee, 1991, Gatlinburg, Tennessee, p. T98.

J. van Schagen, Y. Alhassid, J. Bacelar, B. Bush, M. Harakeh, W. Hesselink, H. Hofmann, N. Kalantar-Nayestanaki, R. Noorman, A. Plompen, A. Stolk, Z. Sujkowski, and A. van der Woude, “GDR dissipation and nuclear shape in hot fast-rotating Dy nuclei,” Physics Letters B, vol. 308, no. 3–4, pp. 231–236. <http://www.sciencedirect.com/science/article/pii/037026939391277T>
The statistical γ-ray decay of the GDR built on excited states in Dy nuclei has been investigated for selected domains of angular momentum up to about 70ħ and temperatures in the range 1–2 MeV. The GDR strength distribution extracted from the data indicate large average nuclear deformations (β ∼ 0.35) at high angular momentum and average temperatures T ⩾ 1.5 MeV. The experimental observation is supported by results from calculations in which thermal shape fluctuations are taken into account around an oblate equilibrium deformation βeq. Although this equilibrium deformation increases with angular momentum, the calculations show rather large and constant average deformations 〈β ∼0.35.

J. van Schagen, Y. Alhassid, J. Bacelar, B. Bush, M. Haraken, W. Hesselink, H. Hofmann, N. Kalantar-Nayestanaki, R. Noorman, A. Plompen, A. Stolk, Z. Sujkowski, and A. van der Woude, “GDR γ-ray decay in 156Dy∗ from regions selected on temperature and angular momentum,” Physics Letters B, vol. 343, no. 1–4, pp. 64–68. <http://www.sciencedirect.com/science/article/pii/037026939401467Q>
The strength distribution of the GDR built on highly excited states in a restricted temperature domain in 156Dy and 155Dy nuclei has been deduced by subtraction of γ-ray spectra obtained for the decay of 154Dy∗ and 156Dy∗ from regions selected on angular momentum. The resulting difference spectra have been analyzed within the statistical model. The results show a large deformation (|β| ∼ 0.51±0.29 and 0.35±0.14) for the angular-momentum regions with 〈J〉 ∼ 32h̵ at T ≈ 1.8±0.2 MeV and 〈J〉 ∼ 46h̵ at T ≈ 1.7±0.2 MeV, respectively, in satisfactory agreement with calculations performed in the framework of Landau theory of shape transitions and statistical fluctuations. The deduced centroid energies are in agreement with the systematics of the GDR built on the ground state. The width of the GDR shows a systematic increase with increasing temperature.