# Mark Caprio

**Associate Professor
Theoretical Physics**

**B.S., (Physics & Mathematics) Oglethorpe University, 1994
M.S., (Physics) Yale University, 1999
M. Phil., (Physics) ibid, 1999
Ph.D., (Physics) ibid, 2003**

E-mail: mcaprio (at) nd.edu

Address: NSH 209

Phone: (574-63)1-2827

Fax: (574-63)1-5952

#### Research Interests

Prof. Caprio’s research emphasis is on nuclear structure theory, including the collective structure of nuclei, Lie algebraic methods, and the nature of phase transitions in quantum many-body systems. He is interested in fundamental problems in the many-body physics of nuclei and other mesoscopic systems, especially the microscopic origins of collective phenomena.

A major outstanding problem in nuclear theory lies in developing the full connection between single-particle and collective degrees of freedom. Fully “microscopic” theories, which treat the nucleus explicitly as a system of nucleons (protons and neutrons), in principle promise to relate nuclear properties directly to the underlying nucleon-nucleon interactions. However, these theories face tremendous computational challenges in properly reproducing collective properties, such as alpha-particle clusters in light nuclei or deformation and surface vibrations in heavier nuclei. At the microscopic level, Prof. Caprio is using Lie algebraic methods to isolate the relevant collective degrees of freedom, with the goal of making the calculation of collective properties a more tractable problem. Prof. Caprio also works extensively with macroscopic models, such as the interacting boson model and geometric model, in which collective features arise through symmetry properties. These descriptions are especially valuable for the phenomenological treatment of nuclear properties of current experimental interest, such as transitions between spherical, deformed, and axially-asymmetric nuclear shapes.

#### Selected Publications

"The Coulomb-Sturmian basis for the nuclear many-body problem," M. A. Caprio, P. Maris, and J. P. Vary, Phys. Rev. C 86, 034312 (2012).

"Dual algebraic structures for the two-level pairing model," M. A. Caprio, J. H. Skrabacz, and F. Iachello, J. Phys. A 44, 075303 (2011).

"Recursive calculation of matrix elements for the generalized seniority shell model," F. Q. Luo and M. A. Caprio, Nucl. Phys. A 849, 35 (2011).

"Racah’s method for general subalgebra chains: Coupling coefficients of SO(5) in canonical and physical bases," M. A. Caprio, K. D. Sviratcheva, and A. E. McCoy, J. Math. Phys. 51, 093518 (2010).

“Bohr model as an algebraic collective model,” D.J. Rowe, T.A. Welsh, and M.A. Caprio, Phys. Rev. C **79**, 054304 (2009). [Synopsis in *Physics: Spotlighting Exceptional Research*]

“Phonon and multi-phonon excitations in rotational nuclei by exact diagonalization of the Bohr Hamiltonian,” M.A. Caprio, Phys. Lett. B **672**, 396 (2009).

“Excited state quantum phase transitions in many-body systems,” M.A. Caprio, P. Cejnar, and F. Iachello, Ann. Phys. (N.Y.) **323**, 1106-1135 (2008).