

The primary goal is the development of a microscopic theory of nuclear collective phenomena aimed at understanding nuclear collective dynamics in terms of interacting neutrons and protons. This goal was identified during 2 1/2 years of graduate studies in Sir Denys Wilkinson’s Department at Oxford and a year with Aage Bohr and Ben Mottelson at the Niels Bohr Institute in Copenhagen. A program of research with the above objectives in mind was formulated during three years with Tony Lane in the Theoretical Physics Division at Harwell. The perspective of nuclear physics acquired during these years was presented in a series of lectures at an International Winter School at Trieste in 1966 and subsequently in a book on Nuclear Collective Motion. The following paragraphs outline primary avenues of research that have proved profitable. An advance came with the discovery that the prevailing manybody theories of equilibrium states and elementary excitations could be expressed succinctly in a socalled equationsofmotion formalism. This formalism embraces HartreeFock mean field theory, the BCS quasiparticle approximation and the Random Phase Approximation within a simple common framework that can be extended and applied more generally. Thus, it provides succinct expressions of standard manybody theories and the means to go beyond them. A second successful approach, known as a theory of largeamplitude collective motion, was
initiated with a graduate student Rick Basserman and subsequently
pursued by many others. The theory was based on the observation that a
submanifold of coherent states of a
manyparticle Hilbert space not only spans the Hilbert space but also
has the properties of a classical phase space. Thus, coherent
states provide a link between classical and quantum
mechanics which make it possible to reduce a complex manybody
quantal system to a more conceptually accessible classical system,
extract a maximally decoupled collective subdynamics, and requantize.
With such objectives in mind, techniques were developed to determine
the valleys, fall lines and ridges of an arbitrary Riemannian manifold
and, hence, distinguish the fast and slow degrees of freedom of a
complex system. Such methods have potential applications to systems
(e.g. atmospheric physics) for which it is desired to reduce the
complexity of the dynamics by averaging over the fast degrees of
freedom. The close relationship between classical and quantal mechanics
defined by coherent state submanifolds has subsequently been explored
in some depth in collaboration with students and associates
(Rosensteel, Ryman, Vassanji, Bartlett) and used to construct explicit
maps from one to the other. Thus, for example, it has been possible to
resolve the ambiguity in Dirac’s canonical quantization procedure. The preceding paragraph shows that the first
essential step towards giving a phenomenological model a microscopic
foundation is to express the model in algebraic terms. This first step
already enables the powerful tools of Lie group and Lie algebra theory
to be utilized in the quantization of the model by construction of the
unitary irreducible representations of its spectrum generating algebra.
Moreover, it is widely applicable because almost all
nuclear models can be expressed as algebraic models.
Expressing the Bohr model as an algebraic
collective model proved to be particularly valuable because it
showed that Bohr model Hamiltonians could be expressed analytically in
terms of SO(5)reduced matrix elements and ClebschGordan coefficients
which made Bohr model calculations very simple to execute. The intriguing journey in pursuit of a microscopic theory of nuclear collective dynamics has followed a path through most of nuclear physics, other areas of physics (e.g., phase transitions, molecular physics, and quantum optics), and some interesting mathematics. Many discoveries and advances have taken place since I embarked on this journey and nuclear physics, in particular, is now in a much more advanced state. Thus, a colleague (John Wood) and I are preparing a twovolume book on "The Fundamentals of Nuclear Models" that will summarize the current state of nuclear structure physics and the experimental and mathematical foundations for the models used to understand it. Hopefully, this text will provide a succinct summary and resource for nuclear physicists wishing to take their subject to the next stage of development and assist researchers in other fields to make use of the methods that have worked so well for one manybody system. The publications listed below include recent papers that can be downloaded and a few selected earlier papers. “CV/#” refers to the document as listed in PDF Curriculum Vitae. Equations of Motion Formalism — back to top “Schematic Interactions for Nuclear Random Phase Approximation Calculations”, D.J. Rowe, Phys. Rev. 162, 866871 (1967). CV/10 pdf “The EquationsofMotion Method and the Extended Shell Model”, D.J. Rowe, Rev. Mod. Phys. 40, 153166 (1968). CV/12 pdf “Methods for calculating groundstate correlations of vibrational nuclei”, D.J. Rowe, Phys. Rev. 175, 12831292 (1968). CV/14 pdf “The OpenShell RandomPhase Approximation and the Negative Parity Excitations of 12C”, D.J. Rowe and S.S.M. Wong, Nucl. Phys. A153, 561585 (1970). CV/21 pdf “Tensor Equations of Motion for the Excitations of Rotationally Invariant or ChargeIndependent Systems”, D.J. Rowe and C. NgoTrong, Rev. Mod. Phys. 47, 471485 (1975). CV/35 pdf “The Tensor OpenShell Random Phase Approximation with Application to the Even Nickel Isotopes”, C. NgoTrong, T. Suzuki and D.J. Rowe, Nucl. Phys. A313, 1544 (1979). CV/56 pdf "An equationsofmotion approach to quantum mechanics: application to a model phase transition", S.Y. Ho, G. Rosensteel, and D.J. Rowe, Phys. Rev. Lett. 98, 080401(14) 2007. CV/184 pdf Large Amplitude
Collective Motion, Coherent States, “Coherent State Theory of Large Amplitude Collective Motion”, D.J. Rowe and R. Basserman, Can. J. Phys. 54, 19411968 (1976). CV/40 pdf “ManyBody Quantum Mechanics as a Symplectic Dynamical System”, D.J. Rowe A.G. Ryman and G. Rosensteel , Phys. Rev. A22, 23622373 (1980). CV/64 pdf “Nondeterminantal HartreeFock theory”, G. Rosensteel and D.J. Rowe, Phys. Rev. A 24, 673679 (1981). CV/68 pdf “Valleys and Fall Lines on a Riemannian Manifold”, D.J. Rowe and A. Ryman, J. Math. Phys. 23, 732735 (1982). CV/70 pdf "Constrained Quantum Mechanics and a Coordinate Independent Theory of the Collective Path'', D.J. Rowe, Nucl. Phys. A 391, 307326 (1982). CV/73 pdf "Density Dynamics: a Generalization of HartreeFock Theory'', D.J. Rowe, M. Vassanji and G. Rosensteel, Phys. Rev. A 28, 19511956 (1983). CV/77 pdf “Classical Dynamics as Constrained Quantum Dynamics”, S.D. Bartlett and D.J. Rowe, J. of Phys. A: Math. Gen. 36, 16831704 (2003). CV/165 pdf Microscopic Theory of Nuclear Collective Dynamics — back to top “Collective Motion in Nuclei and the
Spectrum Generating Algebras T5xSO(3), GL(3,R) and CM(3)”, “Nuclear Sp(3,R) Model”, G. Rosensteel and D.J. Rowe, Phys. Rev. Lett. 38, 1014 (1977). CV/43 pdf “Geometric Derivation of the Kinetic
Energy in Collective Models”, D.J. Rowe and G. Rosensteel, “On the Algebraic Formulation of
Collective Models II: Collective and Intrinsic Submanifolds”, “On the Algebraic Formulation of Collective Models III: the Symplectic Shell Model of Collective Motion”, G. Rosensteel and D.J. Rowe, Annals of Phys. 126, 343370 (1980). CV/62 pdf “The u(3)boson Model of Nuclear Collective Motion”, G. Rosensteel and D.J. Rowe, Phys. Rev. Lett. 47, 223226 (1981). CV/69 pdf “The ShellModel Theory of Nuclear Rotational States”, P. Park, J. Carvalho, M. Vassanji, D.J. Rowe and G. Rosensteel, Nucl. Phys. A414, 93112 (1984). CV/81 pdf “The Geometric SO(3)xD Model: a
Practical
Microscopic Theory of Quadrupole Collective Motion”, “Microscopic Theory of the Nuclear Collective Model”, D.J. Rowe, Rep. Prog. Phys. 48, 14191480 (1985). CV/92 pdf “The Symplectic ShellModel Theory of Collective States”, J. Carvalho, R. Le Blanc, M. Vassanji, D.J. Rowe and J. McGrory, Nucl. Phys. A452, 240262 (1986). CV/94 pdf “Electron Scattering in the Microscopic Sp(3,R) Model”, M. Vassanji and D.J. Rowe, Nucl. Phys. A454, 288300 (1986). CV/96 pdf “Transverse Form Factors in the Collective and Symplectic Models”, M.G. Vassanji and D.J. Rowe, Nucl. Phys. A 618 (1997) 6586. CV/143 pdf “Optimal Basis States for a Microscopic Calculation of Intrinsic Vibrational Wave Functions of Deformed Rotational Nuclei”, M.J. Carvalho, D.J. Rowe, S. Karram, and C. Bahri, Nucl. Phys. A703, 167187 (2002). CV/160 pdf Collective Models as Algebraic Models — back to top “How Do Deformed Nuclei Rotate?”, D.J. Rowe, Nucl. Phys. 152, 273294 (1970). CV/20 pdf “Sum Rule for the Current Density and Nuclear Hydrodynamic Models”, T. Suzuki and D.J. Rowe, Nucl. Phys. A286, 307321 (1977). CV/44 pdf “Group Theoretical Models of Giant Resonance Splittings in Deformed Nuclei”, D.J. Rowe and F. Iachello, Phys. Lett. B130, 231234 (1983). CV/78 pdf “Dynamical Symmetries of Nuclear Collective Models”, D.J. Rowe, Prog. in Part and Nucl. Phys. 37, 265 (1996). CV/141 pdf “Transverse Form Factors in the Collective and Symplectic Models”, M.J. Carvalho and D.J. Rowe, Nucl. Phys. A618, 6586 (1997). CV/143 pdf “An Algebraic Representation of the ParticleplusRotor Model”, H. de Guise and D.J. Rowe, Nucl. Phys. A 636 (1998) 4769. CV/147 pdf “RotationVibratIonal Spectra of Diatomic Molecules and Nuclei with Davidson Interactions”, D.J. Rowe and C. Bahri, J. Phys. A31, 49474961 (1998). CV/148 pdf “A Computationally Tractable Version of the Collective Model”, D.J. Rowe, Nucl. Phys. A 735, 372392 (2004). CV/167. pdf "Spherical harmonics and basic
ClebschGordan coefficients for the group SO(5) in an SO(3) “The algebraic collective model”, D.J. Rowe and P.S. Turner, Nucl. Phys. A 753, 94105 (2005). CV/173. pdf “On the many relationships between the IBM and Bohr model”, D.J. Rowe and G. Thiamova, Nucl. Phys. A 760, 5981 (2005). CV/176 pdf "An algebraic approach to problems with polynomial Hamiltonians on Euclidean spaces", D.J. Rowe, J. Phys. A: Math. Gen. 38, 1018110201 (2005). CV/178 pdf "Construction of SO(5) spherical harmonics and ClebschGordan coefficients", M.A. Caprio, D.J. Rowe and T.A. Welsh, Compt. Phys. Commun., 180, 11501163 (2009). CV/188 pdf "Bohr model as an algebraic collective model", D.J. Rowe, T.A. Welsh and M.A. Caprio, Phys. Rev. C 79, 054304(116) (2009). CV/189 pdf Vector Coherent State Theory and other Mathematical Physics — back to top “Coherent State Theory of the NonCompact Symplectic Group”, D.J. Rowe, J. Math. Phys. 25, 26622671 (1984). CV/84 pdf “Vector Coherent State Representation Theory”, D.J. Rowe, G. Rosensteel and R. Gilmore, J. Math. Phys. 26, 27872791 (1985). CV/87 pdf “Unitary Representations, Branching Rules and Matrix Elements for the NonCompact Symplectic Groups”, D.J. Rowe, B.G. Wybourne and P.H. Butler, J. Phys. A: Math. Gen. 18, 939953 (1985). CV/90 pdf “Decomposition of the SO*(8) Enveloping Algebra under U(4) > U(3)”, R. Le Blanc and D.J. Rowe, J. Math. Phys. 28, 12311236 (1987). CV/103 pdf “HeisenbergWeyl Algebras of Symmetric and AntiSymmetric Bosons”, R. Le Blanc and D.J. Rowe, J. Phys. A: Math. Gen. 20, L681687 (1989). CV/105 pdf “Vector Coherent State Theory and its Applications to the Orthogonal Groups”, D.J. Rowe, R. Le Blanc and K.T. Hecht, J. Math. Phys. 29, 287304 (1987). CV/107 pdf “The Matrix Representations of g_2: I. Representations in an SO(4) basis”, R. Le Blanc and D.J. Rowe, J. Math. Phys. 29, 758766 (1988). CV/109 pdf “The Matrix Representations of g_2: II. Representations in an SU(3) basis”, R. Le Blanc and D.J. Rowe, J. Math. Phys. 29, 767776 (1988). CV/110 pdf “Highest Weight Representations for gl(m/n) and gl(m+n)”, R. Le Blanc and D.J. Rowe, J. Math. Phys. 30, 14151432 (1989). CV/115 pdf “A Rotor Expansion of the su(3) Lie Algebra”, D.J. Rowe, R. Le Blanc and J. Repka, J. Phys. A: Math. Gen. 22, L309316 (1989). CV/116 pdf “The CoupledRotorVibrator Model”, D.J. Rowe, M. Vassanji and J. Carvalho, Nucl. Phys. A504, 76102 (1989). CV/117 pdf “Superfield and Matrix Realizations of Highest Weight Representations for osp(m/2n)”, R. Le Blanc and D.J. Rowe, J. Math. Phys. 31, 1436 (1990). CV/118 pdf “VectorCoherentState Theory as a Theory of Induced Representations”, D.J. Rowe and J. Repka, J. Math. Phys. 32, 26142634 (1991). CV/125 pdf “Resolution of Missing Label Problems; a New Perspective on KMatrix Theory”, D.J. Rowe, J. Math. Phy. 36, 152030 (1995). CV/136 pdf “Induced Shift Tensors in Vector Coherent State Theory”, D.J. Rowe and J. Repka, J. Math. Phys. 36, 200829 (1995). CV/137 pdf “Representation of the FveDimensional Harmonic Oscillator with ScalarValued U(5) > SO(5) > SO(3)Coupled VCS Wave Functions”, D.J. Rowe and K.T. Hecht, J. Math. Phys. 36, 471134 (1995). CV/139 pdf “Asymptotic ClebschGordan Coefficients”, H. de Guise and D.J. Rowe, J. Math. Phys. 36 (1995) 69917008. CV/140 pdf “The RacahWigner Algebra and Coherent Tensors”, D.J. Rowe and J. Repka, J. Math. Phys. 37 (1996) 24982510. CV/142 pdf “The Representations and Coupling Coefficients of su(n); Application to su(4)”, D.J. Rowe and J. Repka, J. Foundations of Physics 27, (1997) 11791209. CV/145 pdf “ClebschGordan Coefficients in the Asymptotic Limit”, H. de Guise and D.J. Rowe, J. Math. Phys. 39 (1998) 10871106. CV/146 pdf “Branching Rules for Restriction of the Weil Representations of Sp(n,R) to its Maximal Parabolic Subgroup CM(n)”, D.J. Rowe and J. Repka, J. Math. Phys. 39, 621424 (1998). CV/151 pdf “Representations of the Weyl Group and Wigner Functions for SU(3)”, D.J. Rowe, B.C. Sanders and H. de Guise, J. Math. Phys. 40, 36043615 (1999). CV/152 pdf “Vector Phase Measurement in Multipath Quantum Interferometry, B.C. Sanders, H. de Guise, D.J. Rowe and A. Mann, J. Phys. A: Math. Gen. 32 (1999) 77917801. CV/153 pdf “Angularmomentum Projection of Rotational Model Wave Functions”, D.J. Rowe, S. Bartlett, and C. Bahri, Phys. Lett. B472, 227231 (2000). CV/155 pdf “ClebschGordan Coefficients of SU(3) in SU(2) and SO(3) bases”, D.J. Rowe and C. Bahri, J. Math. Phys. 41 (2000) 65446565. CV/156 pdf “Asymptotic Limits of SU(2) and SU(3) Wigner Functions”, D.J. Rowe, H. De Guise, and B.C. Sanders, J. Math. Phys. 42 (2001) 23152342. CV/157 pdf “VCS Representations, Induced Representations, and Geometric Quantization: I. Scalar Coherent State Representations”, S.D. Bartlett, D.J. Rowe, and J. Repka, J. of Phys. A: Math. Gen. 35, 5599624 (2002). CV/161 pdf “VCS representations, Induced Representations, and Geometric Quantization: II. Vector Coherent State Representations”, S.D. Bartlett, D.J. Rowe, and J. Repka, J. of Phys. A: Math. Gen. 35, 562551 (2002). CV/162 pdf “Coherent State Triplets and their Inner Products”, D.J. Rowe and J. Repka, J. Math. Phys. 43, (2002) 540038. CV/163 pdf “Efficient Sharing of a Continuous Quantum Secret”, T. Tyc, D.J. Rowe and B.C. Sanders, J. of Phys. A: Math. & Gen. 36, 762537 (2003). CV/166 pdf “Programs for generating
ClebschGordan
coefficients of SU(3) in SU(2) and SO(3) bases”, C. Bahri,
D.J.
Rowe, and J.P. Draayer, Compt. Phys. Commun. 159, 121143 (2004). CV/168 pdf “Spherical harmonics and basic
ClebschGordan coefficients for the group SO(5) in an SO(3)
basis”,
D.J. Rowe, P.S. Turner, and J. Repka, J. Math. Phys. 45, 276184
(2004). CV/169 pdf “Vector coherent theory of the generic representations of so(5) in an so(3) basis”, P.S. Turner, D.J. Rowe, and J. Repka, J. Math. Phys. 47, 023507(125) (2006). CV/179 pdf Shell Model and Coupling Schemes — back to top “A Perturbative Analysis of Linked and Unlinked TwoBody Effective Interactions Obtained from large Matrix Diagonalizations,” N. Lo Iudice, D.J. Rowe and S.S.M. Wong, Nucl. Phys. A 297, 3544 (1978). CV/54 pdf “A Unified PairCoupling Theory of Fermion Systems,” D.J. Rowe, T. Song and H. Chen, Phys. Rev. C44, R598601 (1991). CV/124 pdf “The Role of Spin in the Strong Coupling of a Rotor and Single Particle”, H. de Guise, D.J. Rowe and R. Okamoto, Nucl. Phys. A 575 (1994) 4660. CV/133 pdf “The Pair Coupling Model”, H. Chen, T. Song and D.J. Rowe, Nucl. Phys. A582, 181204 (1995). CV/135 pdf “Restoration of Particle Number as a Good Quantum Number in BCS Theory”, D.J. Rowe, Nucl. Phys. A691, 691709 (2001). CV/158 pdf “Partially Solvable PairCoupling Models with SeniorityConserving Interactions”, D.J. Rowe and G. Rosensteel, Phys. Rev. Lett. 87, 172501 14 (2001). CV/159 pdf “SeniorityConserving Forces and
USp(2j+1)
Partial Dynamical Symmetry”, G. Rosensteel and D.J. Rowe, Phys.
Rev.
C67, 014303 (2003). CV/164 pdf “Implications of shape coexistence
for the
nuclear shell model”, D.J. Rowe, G. Thiamova, and “Duality relationships and supermultiplet symmetry in the O(8) paircoupling model”, D.J. Rowe and M.J. Carvalho, J. Phys. A: Math. Theor. 40, 471500 (2007). CV/183 pdf QuasiDynamical Symmetry and Phase Transitions — back to top “Dynamic Structure and Embedded Representations in Physics: the Group Theory of the Adiabatic Approximation”, D.J. Rowe, P. Rochford and J. Repka, J. Math. Phys. 29, 572577 (1988). CV/108 pdf “The Survival of SU(3) Bands under Strong SpinOrbit Symmetry Mixing”, P. Rochford and D.J. Rowe, Phys. Lett. B210, 59 (1988). CV/111 pdf “Model of a Superconducting Phase Transition”, H. Chen, J. Brownstein and D.J. Rowe, Phys. Rev. C42, 142231 (1990). CV/121 pdf “The SU(3) Structure of Rotational States in Heavy Deformed Nuclei”, M. Jarrio, J.L. Wood and D.J. Rowe, Nucl. Phys. A528, 409435 (1991). CV/123 pdf “Phase Transitions in the PairingplusQuadrupole Model”, C. Bahri, D.J. Rowe, and W. Wijesundera, Phys. Rev. C58, 1539 (1998). CV/150 pdf “SU(3) QuasiDynamical Symmetry as
an
Organizational Mechanism for Generating Nuclear Rotational
Motions”, C.
Bahri and D.J. Rowe, Nucl. Phys. A662, 125147 (2000). CV/154 pdf “Quasi dynamical symmetry in an
interacting boson model phase transition”, D.J. Rowe, Phys. Rev.
Lett. 93, 122502 (2004). CV/170 pdf “Phase transitions and quasidynamical symmetry in nuclear collective models: I. The U(5) to O(6) phase transition in the IBM”, D.J. Rowe, Nucl. Phys. A 745, 4778 (2004). CV/171 pdf “Scaling properties and asymptotic spectra of finite models of phase transitions as they approach macroscopic limits”, D.J. Rowe, P.S. Turner and G. Rosensteel, Phys. Rev. Lett. 93, 232502 (2004). CV/172 pdf “Phase transitions and
quasidynamical
symmetry in nuclear collective models: II. The
sphericalvibrator to gammasoftrotor phase transition in an
SO(5)invariant Bohr model”, P.S. Turner and D.J. Rowe,
Nucl.
Phys. A 756, 333355 (2005). CV/173 pdf “Phase transitions and quasidynamical symmetry in nuclear collective models: III. U(5) to SU(3) phase transition in the IBM”, G. Rosensteel and D.J. Rowe, Nucl. Phys. A 759, 92128 (2005). CV/175 pdf Books — back to top "Nuclear Collective Motion'', (Methuen, London, 1970) pp. 340. "The Shell Model Theory of Nuclear Collective States" in Dynamical Groups and Spectrum Generating Algebras, eds. A. Bohm, Y. Ne'eman, A.O. Barut, World Scientific 1988, vol. I, pp 287315. "Mathematical Physics" in Physics 2000 as it Enters a New Millennium, eds. P.J. Black. G.W.F. Drake, and L. Jossem (I.U.P.A.P. 36) pp 106116. pdf "Practical Group Theory" (in preparation with Joe Repka). "Fundamentals of Nuclear Models" (with J.L. Wood), in press. 

