Short timescale behavior of colliding heavy nuclei at intermediate energies

An Antisymmetrized Molecular Dynamics model is used to explore the collision of $^{114}$Cd projectiles with $^{92}$Mo target nuclei at E/A=50 MeV over a broad range in impact parameter. The atomic number (Z), velocity, and emission pattern of the reaction products are examined as a function of the impact parameter and the cluster recognition time. The non-central collisions are found to be essentially binary in character resulting in the formation of an excited projectile-like fragment (PLF$^*$) and target-like fragment (TLF$^*$). The decay of these fragments occurs on a short timescale, 100$\le$t$\le$300 fm/c. The average excitation energy deduced for the PLF$^*$ and TLF$^*$ `saturates for mid-central collisions, 3.5$\le$b$\le$6 fm, with its magnitude depending on the cluster recognition time. For short cluster recognition times (t=150 fm/c), an average excitation energy as high as $\approx$6 MeV is predicted. Short timescale emission leads to a loss of initial correlations and results in features such as an anisotropic emission pattern of both IMFs and alpha particles emitted from the PLF$^*$ and TLF$^*$ in peripheral collisions.Comment: 19 pages, 17 figure

On the p-adic geometry of traces of singular moduli

The aim of this article is to show that p-adic geometry of modular curves is useful in the study of p-adic properties of traces of singular moduli. In order to do so, we partly answer a question by Ono. As our goal is just to illustrate how p-adic geometry can be used in this context, we focus on a relatively simple case, in the hope that others will try to obtain the strongest and most general results. For example, for p=2, a result stronger than Thm.1 is proved in [Boylan], and a result on some modular curves of genus zero can be found in [Osburn] . It should be easy to apply our method, because of its local nature, to modular curves of arbitrary level, as well as to Shimura curves.Comment: 3 pages, Late

Magnetic-Field Induced Gap in One-Dimensional Antiferromagnet KCuGaF6_6

Magnetic susceptibility and specific heat measurements in magnetic fields were performed on an $S=1/2$ one-dimensional antiferromagnet KCuGaF$_6$. Exchange interaction was evaluated as $J/k_{\rm B}\simeq 100$ K. However, no magnetic ordering was observed down to 0.46 K. It was found that an applied magnetic field induces a staggered magnetic susceptibility obeying the Curie law and an excitation gap, both of which should be attributed to the antisymmetric interaction of the Dzyaloshinsky-Moriya type and/or the staggered $g$-tensor. With increasing magnetic field $H$, the gap increases almost in proportion to $H^{2/3}$.Comment: Submitted to Proceedings of Research in High Magnetic Fiel

Antisymmetrized molecular dynamics with quantum branching processes for collisions of heavy nuclei

Antisymmetrized molecular dynamics (AMD) with quantum branching processes is reformulated so that it can be applicable to the collisions of heavy nuclei such as Au + Au multifragmentation reactions. The quantum branching process due to the wave packet diffusion effect is treated as a random term in a Langevin-type equation of motion, whose numerical treatment is much easier than the method of the previous papers. Furthermore a new approximation formula, called the triple-loop approximation, is introduced in order to evaluate the Hamiltonian in the equation of motion with much less computation time than the exact calculation. A calculation is performed for the Au + Au central collisions at 150 MeV/nucleon. The result shows that AMD almost reproduces the copious fragment formation in this reaction.Comment: 24 pages, 5 figures embedde

Proof of the Umbral Moonshine Conjecture

The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock modular forms. Gannon has proved this for the special case involving the largest sporadic simple Mathieu group. Here we establish the existence of the umbral moonshine modules in the remaining 22 cases.Comment: 56 pages, to appear in Research in the Mathematical Science

Pariah moonshine

Finite simple groups are the building blocks of finite symmetry. The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah groups which do not belong to any of the natural families, and are not involved in the monster. It also precipitated monstrous moonshine, which is an appearance of monster symmetry in number theory that catalysed developments in mathematics and physics. Forty years ago the pioneers of moonshine asked if there is anything similar for pariahs. Here we report on a solution to this problem that reveals the O'Nan pariah group as a source of hidden symmetry in quadratic forms and elliptic curves. Using this we prove congruences for class numbers, and Selmer groups and Tate--Shafarevich groups of elliptic curves. This demonstrates that pariah groups play a role in some of the deepest problems in mathematics, and represents an appearance of pariah groups in nature.Comment: 20 page

Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation

On the basis of the antisymmetrized molecular dynamics (AMD) of wave packets for the quantum system, a novel model (called AMD-V) is constructed by the stochastic incorporation of the diffusion and the deformation of wave packets which is calculated by Vlasov equation without any restriction on the one-body distribution. In other words, the stochastic branching process in molecular dynamics is formulated so that the instantaneous time evolution of the averaged one-body distribution is essentially equivalent to the solution of Vlasov equation. Furthermore, as usual molecular dynamics, AMD-V keeps the many-body correlation and can naturally describe the fluctuation among many channels of the reaction. It is demonstrated that the newly introduced process of AMD-V has drastic effects in heavy ion collisions of 40Ca + 40Ca at 35 MeV/nucleon, especially on the fragmentation mechanism, and AMD-V reproduces the fragmentation data very well. Discussions are given on the interrelation among the frameworks of AMD, AMD-V and other microscopic models developed for the nuclear dynamics.Comment: 26 pages, LaTeX with revtex and epsf, embedded postscript figure

Compatibility of localized wave packets and unrestricted single particle dynamics for cluster formation in nuclear collisions

Antisymmetrized molecular dynamics with quantum branching is generalized so as to allow finite time duration of the unrestricted coherent mean field propagation which is followed by the decoherence into wave packets. In this new model, the wave packet shrinking by the mean field propagation is respected as well as the diffusion, so that it predicts a one-body dynamics similar to that in mean field models. The shrinking effect is expected to change the diffusion property of nucleons in nuclear matter and the global one-body dynamics. The central \xenon+\tin collisions at 50 MeV/nucleon are calculated by the models with and without shrinking, and it is shown that the inclusion of the wave packet shrinking has a large effect on the multifragmentation in a big expanding system with a moderate expansion velocity.Comment: 16 pages, 7 figure