Optimal Linear Glauber Model

Contrary to the actual nonlinear Glauber model, the linear Glauber model (LGM) is exactly solvable, although the detailed balance condition is not generally satisfied. This motivates us to address the issue of writing the transition rate () in a best possible linear form such that the mean squared error in satisfying the detailed balance condition is least. The advantage of this work is that, by studying the LGM analytically, we will be able to anticipate how the kinetic properties of an arbitrary Ising system depend on the temperature and the coupling constants. The analytical expressions for the optimal values of the parameters involved in the linear are obtained using a simple Moore-Penrose pseudoinverse matrix. This approach is quite general, in principle applicable to any system and can reproduce the exact results for one dimensional Ising system. In the continuum limit, we get a linear time-dependent Ginzburg-Landau equation from the Glauber's microscopic model of non-conservative dynamics. We analyze the critical and dynamic properties of the model, and show that most of the important results obtained in different studies can be reproduced by our new mathematical approach. We will also show in this paper that the effect of magnetic field can easily be studied within our approach; in particular, we show that the inverse of relaxation time changes quadratically with (weak) magnetic field and that the fluctuation-dissipation theorem is valid for our model.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.

The properties of halo structure for B-17

The total reaction cross section (1724 +/- 93 mb) of B-17 at the energy of 43.7 A MeV on C target has been measured by using the transmission method at the Radioactive Ion Beam Line in Lanzhou (RIBLL). Assuming B-17 consists of a core B-15 plus two halo neutrons, the total cross section of B-17 on C target was calculated with the zero-range Glauber model, where double Gaussian density distributions and Gaussian plus HO density distributions were used. It can fit the experimental data very well. The characteristic of halo structure for B-17 was found with a large diffusion of the neutrons density distribution.

Studies on the exotic structure of Al-23

The longitudinal momentum distribution (P-//) of fragments after one-proton removal from Al-23 and reaction cross sections (sigma(R)) for Al-23,Al-24 on carbon target at 74A MeV have been measured simultaneously. An enhancement in sigma(R) is observed for Al-23 compaxed with Al-24. The full width at half maximum of the P-// distribution for Mg-22 fragments has been determined to be 232 +/- 28 MeV/c. Analysis of P-// using the Few-Body Glauber Model indicates a dominant d-wave configuration for the valence proton in the ground state of Al-23. The exotic structure in Al-23 is discussed.

Measurement of total reaction cross section for neutron-rich nucleus Li-11 on Si-28 target at medium energy

The neutron-rich nucleus Li-11 is separated by the radioactive ion beam line RIBLL at HIRFL from the breakup of 50MeV/u C-13 on Be target. The total reaction cross sections for Li-11 at energies range from 25 to 45MeV/u on Si target have been measured by using the transmission method. The experimental data at high and low energies can be fitted well by Glauber model using two Gauss density distribution. The matter radius of Li-11 was also deduced.

Measurement of the total reaction cross section for the mirror nuclei N-12 and B-12

The mirror nuclei N-12 and B-12 are separated by the Radioactive Ion Beam Line in Lanzhou (RIBLL) at HIRFL from the breakup of 78.6 MeV/u N-14 on a Be target. The total reaction cross-sections of N-12 at 34.9 MeV/u and B-12 at 54.4 MeV/u on a Si target have been measured by using the transmission method. Assuming N-12 consists of a C-11 core plus one halo proton, the excitation function of N-12 and B-12 on a Si target and a C target were calculated with the Glauber model. It can fit the experimental data very well. The characteristic halo structure for N-12 was found with a large diffusion of the protons density distribution.

Experimental Study on the Exotic Structure of N-12 in RIBLL

We measured the total reaction cross sections of N-12 in Si at 36.2 MeV/u. using Radioactive Ion Beam Line in Lanzhou (RIBLL) with a new method. The reaction target was installed at the intermediate focusing point T1 at RIBLL. This scheme allows us to identify particles before and after the reaction target unambiguously. The total reaction cross section (1760 +/- 78mb) of N-12 in Si is obtained. Assuming that N-12 consists of a core C-11 plus one halo proton, the excitation function of N-12 on the Si and C targets is calculated with the Glauber model and the Fermi-Fermi density distributions. It can fit the experimental data very well. A large diffusion of the protons density distribution supports the halo structure for N-12.

Ultra peripheral heavy ion collisions and the energy dependence of the nuclear radius

To estimate realistic cross sections in ultra peripheral heavy ion collisions we must remove effects of strong absorption. One method to eliminate these effects make use of a Glauber model calculation, where the nucleon-nucleon energy dependent cross sections at small impact parameter are suppressed. In another method we impose a geometrical cut on the minimal impact parameter of the nuclear collision ((b)min > R-1 + R-2, where R-i is the radius of ion 'i'). In this last case the effect of a possible nuclear radius dependence with the energy has not been considered in detail up to now. Here we introduce this effect showing that for final states with small invariant mass the effect is negligible. However when the final state has a relatively large invariant mass, e.g., an intermediate mass Higgs boson, the cross section can decrease up to 50%. (C) 2003 Published by Elsevier B.V.