Quantal Bits

F. S. Levin

Ivars Peterson

Zafar Ahmed, Sudhir R Jain

Based on extraction of resonances from quantal time delay, a theorem relating quantal time delay and the number of resonances below a certain energy is proved here. Several illustrations from quantum mechanics, neutron reflectometry and hadron resonances are presented.

D. Vrinceanu, M. Raymond Flannery

The classical form factor is deduced from exact correspondence with a phase-space representation of the quantal form factor. Analytical expressions are provided for $n\stackrel{\ensuremath{\rightarrow}}{l}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}},$ $n\stackrel{\ensuremath{\rightarrow}}{l}{n}^{\ensuremath{'}}$, and $\stackrel{\ensuremath{\rightarrow}}{n}{n}^{\ensuremath{'}}$ transitions in hydrogenic systems and for $\stackrel{\ensuremath{\rightarrow}}{n}{n}^{\ensuremath{'}}$ in the one-dimensional harmonic oscillator. An efficient procedure for calculation of quantal form factors as analytical functions of momentum transfer, for arbitrary quantum numbers, is presented. The classical approach has the ability to explain quite succinctly interesting trends and various important aspects which remain hidden within the quantal treatment of form factors. The classical-quantal comparison ranges from being qualitatively good for $n\stackrel{\ensuremath{\rightarrow}}{l}{n}^{\ensuremath{'}}{l}^{\ensuremath{'}}$ transitions to close agreement for $n\stackrel{\ensuremath{\rightarrow}}{l}{n}^{\ensuremath{'}}$ and $\stackrel{\ensuremath{\rightarrow}}{n}{n}^{\ensuremath{'}}$ transitions. Excellent agreement is obtained for the integrated form factor for all transitions.

Valerie Min Ye

J.-P. Ebran, Louis Heitz, Elias Khan

The use of quantality is discussed in the case of nuclei and other many-body systems such as atomic electrons. This dimensionless quantity is known to indicate when a many-body system behaves like a crystal or a quantum liquid. Its role is further analyzed by showing its relation to the scattering length. The emergence of a fundamental length scale, the limit radius, is also shown. It corresponds to the hard-core of the nucleon-nucleon interaction in the case of nucleons, and to a value close to the Bohr radius in the case of atomic electrons. The occurrence of a cluster phase in nuclei is analyzed using the quantality through its relation to the localization parameter, allowing for the identification of both the number of nucleons and the density as control parameters for the occurrence of this phase. The relation of the quantality to the magnitude of the interaction also exhibits a third dimensionless parameter, monitoring the magnitude of the spin-orbit effect in finite systems, through the realization of the pseudospin symmetry. The impact of quantality on the spin-orbit effect is compared in various many-body systems. The role of quantality in the relative effect of the binding energy and the shell one is also analyzed in nuclei. Finally, additional dimensionless quantities are proposed from the generalization of the quantality. Nuclei are found to be exceptional systems because all their dimensionless quantities are close to the order of unity, at variance with other many-body systems.