Nuclear Structure at Low Spins

Collective modes, their evolution and their relation to the underlying shell structure
 
 

The study of the evolution of collectivity in nuclei is a major focus of the low spin nuclear structure research carried out at WNSL. Current research centers on such questions as:
 

· The nature of vibrational excitations

· The existence of multi-phonon states and the role of the Pauli Principle

· Phase transitions in finite nuclei

· Q-invariants

· Evolution of collectivity and valence correlation schemes

· Tests of the Geometric Collective Model

· Study of exotic nuclei with radioactive beams
 
 
 
 

The nature of vibrational excitations

The fundamental excitations of atomic nuclei fall into two classes — single particle excitations in which individual nucleons change orbits and collective excitations involving the coherent motions of many nucleons. The latter can be pictured as rotations and vibrations of the nucleus. Several different types of vibrational excitations have been discovered but, remarkably, their nature is not at all well understood.

We use the tandem accelerator to produce nuclei in these excitation states and then study their g -decay. We exploit an instrument called a Moving Tape Collector, with microprocessor control, to isolate source activities of appropriate nuclei to study their nuclear transitions with state-of-the-art arrays of g -ray detectors. These studies can improve on existing data by orders-of-magnitude. We then interpret the data with various collective models of nuclear excitations.
 

Multi-phonon states

A fundamental issue for any many-body system of strongly interacting fermions is the interplay of collective and single-particle degrees of freedom. Collective vibrational (phonon) modes are constructed from excitations of nucleons from one orbit to another. Each type of phonon will be different in structure depending on the characteristic orbits involved and will evolve differently in energy and excitation strength with neutron and proton number. But the Pauli Principle limits the number of fermions in a given orbit. In nuclear states consisting of superpositions of many phonons, there is a continual struggle between the Pauli Principle and the survival of collectivity in these states. This strikes at the heart of the issue of understanding the coherent motion of nucleons in the nucleus.
 
 

At WNSL we have an active program to measure the properties of multi-phonon states using nuclear reactions to make these states and g -ray detectors from YRAST Ball to study their decay. The picture below illustrates the concept of phonon or multi-phonon excitations, a possible signature that we can experimentally test, and an example for a reaction process involved.

Phase transitions in finite nuclei

It has long been thought that atomic nuclei (with finite numbers of nucleons) cannot exhibit true phase transitional behavior such as is seen in condensed matter and magnetic systems. Yet recent discoveries at WNSL challenge these preconceptions with evidence that such phase transitions do exist. Indeed, an example of phase coexistence has been identified, in the nucleus ¹⁵²Sm. These results are leading to significant revisions in our understanding of nuclei  and the structural evolution as as function of nucleon number. They have spawned a new research program at Yale involving measurements of g -ray decay transitions, nuclear level lifetimes, and transition rates, in key nuclei where phase transitional behavior is suspected.
 
 

Collective structure and Q-invariants

In an approach to nuclear structure called the Q-invariant approach one can express key physical quantities (such as the deformation parameters of the nuclear ellipsoid or their stiffness) in terms of model-independent sums of complete sets of transition intensities. Although this is not in itself a new idea, it is only recently that it has been realized that it is not necessary to have a full knowledge of transition rates for every state in order to apply these theorems. Thus it becomes possible to make practical estimates of important physical quantities based on information gained in fairly simple measurements of transitions rates for a few low-lying states. This has important applications to newly accessible exotic nuclei where data will be scarce.
 

Evolution of collectivity

Over the last years members of the WNSL group have pioneered a powerful approach to structural evolution by studying the changing properties in terms of correlations of collective observables, either with extrinsic variables such as the valence nucleon number product N_pN_n or the related P-factor, or with intrinsic variables such as other collective observables. A part of the experimental program focuses on studying new nuclei where very little experimental information is known and where new data can test these correlation schemes and relate the onset of collectivity and the behavior of phase/shape transitional regions to the underlying shell structure.
 

Test of the Geometric Collective Model
 

There are very few nuclear models that are efficient and practical for the study of heavy collective nuclei. One such model is the Geometric Collective Model (GCM) which utilizes a potential well specified in terms of the shape of the nucleus. Unfortunately, the Hamiltonian contains 8 separate terms (two kinetic energy terms and a 6-term anharmonic potential) and therefore it has rarely been exploited.

We have recently developed a highly simplified version of this model and are applying it to study the evolution of nuclear structure and the nature of its fundamental coherent excitation modes. Areasof interest are the treatment of transitional nuclei, the nature of Q-invariants in the model, and the study of remarkable regularities in the structural evolution.
 
 

The study of exotic nuclei with radioactive beams
 

The newest frontier in nuclear physics is the study of new horizons of the nuclear landscape: that is, the formation and study of exotic nuclei with extreme ratios of neutron and proton numbers. These nuclei, studied at radioactive beam facilities, are revealing phenomena unlike any yet seen in nuclei. The WNSL group has had a long interest and a distinguished leadership role in the RNB field. Most of this work centers on outside facilities such as HRIBF, MSU and TRIUMF.

As part of a coherent research effort using Coulomb excitation, we are carrying out a program of low energy Coulomb excitation in inverse kinematics at RNB facilities, using the GRAFIK family of detectors. The aim is to study the lowest one or two excited states in collective nuclei in order to map out and understand the evolution and origins of collectivity both near and far from stability. Coulomb excitation is used since it is a clean, well-understood mechanism below the Coulomb barrier. Low RNB energies (1.5-3 MeV/A) are used so that only the lowest one or two states are excited and only one or two matrix elements, corresponding to excitations of the lowest states, are involved. Finally, inverse kinematics is critical so that the radioactivity can be deposited downstream and, in the lifetime method, forward focussing is essential to obtain a tight correlation of distance and time.