Excited States

Giampaolo Co’

Xiaoguang Wang, Hong‐Chen Fu

We introduce excited binomial states and excited negative binomial states of the radiation field by repeated application of the photon creation operator on binomial states and negative binomial states. They reduce to Fock states and excited coherent states in certain limits and can be viewed as intermediate states between Fock states and coherent states. We find that both the excited binomial states and excited negative binomial states can be exactly normalized in terms of hypergeometric functions. Base on this interesting character, some of the statistical properties are discussed.

Th. Popa, Nicolae Sandulescu, Michelangelo Sambataro

We study the excited states of zero seniority for various like-particle systems interacting by pairing forces and by general two-body interactions. We consider two types of excitations, generated from a ground state described by a pair condensate. One type is obtained by breaking a pair from the ground-state condensate and replacing it by ``excited'' collective pairs built on time-reversed single-particle orbits. The second type of zero-seniority excited states is described by a condensate of identical excited pairs. The structure of these excited states is analyzed for the picket fence model and for the valence neutrons of $^{108}\mathrm{Sn}$. For a state-depending pairing interaction, the first type of excited states agree well with the $J=0$ states which are known in $^{108}\mathrm{Sn}$. At the same time, these states can be also associated unambiguously with those exact states which are the closest in energy to the experimental levels. The states corresponding to the excited pair condensate (EPC) appear at low energies, around the energy of the second-excited state of the first type, and they do not have a simple correspondence with exact eigenstates. However, at a much higher excitation energy there is an exact state which is similar in structure to an EPC state. It is shown that this EPC state has the features of a giant pairing vibration.

Anonymous

Y. M. Cheung, Swapan Kumar Gayen

The optical-absorption transitions originating from the lowest 4f5d excited state of ${\mathrm{Pr}}^{3+}$ in ${\mathrm{Y}}_{3}$${\mathrm{Al}}_{5}$${\mathrm{O}}_{12}$ have been studied. The experimental arrangement uses a 7-ns 266-nm light pulse to populate the lowest 4f5d state, and a spatially overlapped, time-sequenced pulse from a frequency-tunable dye laser to induce transitions from that excited state. The excited-state-absorption (ESA) spectrum covering the 900--300-nm probe wavelength range is characterized by two broad peaks centered at 700 and 350 nm on a slowly rising background. The peak ESA cross section at 355 nm is (1\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}17}$ ${\mathrm{cm}}^{2}$. The position, shape, and strength of the spectrum suggest that the terminal states of the ESA transitions are the second 4f5d state of ${\mathrm{Pr}}^{3+}$ and the conduction band of the host lattice. The ESA measurements have been extended to transitions from the $^{3}$${\mathit{P}}_{0}$ and $^{1}$${\mathit{D}}_{2}$ excited states of the 4${\mathit{f}}^{2}$ configuration of ${\mathrm{Pr}}^{3+}$ as well. The ESA cross sections at a probe wavelength of 532 nm are (8\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$ ${\mathrm{cm}}^{2}$ and (5.7\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$ ${\mathrm{cm}}^{2}$ for transitions from the $^{3}$${\mathit{P}}_{0}$ and $^{1}$${\mathit{D}}_{2}$ excited states, respectively. The terminal state of ESA transitions from these two levels is the lowest 4f5d state. The strong ESA completely inhibits the potential laser action based on emission from these states in this crystal.

Karl Taylor Compton