High-spin physics

High-spin physics comprises physical phenomena observed when atomic nuclei are in quantal states with high angular momentum (high spin).
High-spin states of atomic nuclei can be generated in two fundamental ways. The first appears in nearly spherical nuclei. Here, they are formed from excitations of few particles that align their spin vectors step by step. This leads to an irregular level structure: the level energy E is not proportional to the spin J. See an example. The second occurs in deformed nuclei. The entire nucleus can rotate about an axis perpendicular to the symmetry axis. This leads to a regular level structure (a rotational band): E ˜ J(J+1). See an example. As many particles contribute to this kind of rotation, we call it collective rotation.

The atomic nucleus is a quantum-mechanical many-body system. The understanding of such systems is one of the important questions of modern physics.
The nucleus consists of protons and neutrons, called nucleons. The nucleus of the lightest element, hydrogen, can exist in two stable isotopes: it consists either of one proton only (normal hydrogen) or of one proton and one neutron (deuterium). The heaviest nuclei consist of about 100 protons and about 150 neutrons. The nucleus occupies a unique position in nature, since it allows us to study phenomena of a quantum many-body system for specific numbers of particles (nucleons). These numbers may be small enough to study properties based on the motion of single nucleons. On the other hand, the particle numbers may be large enough for a collective motion of many nucleons that appears as a rotation or vibration of the entire nucleus.
The study of these phenomena of the nuclear many-body system requires the knowledge of the excited states of nuclei up to high excitation energy and high spin.

How can we excite high-spin states of nuclei?

Excited states in a nucleus can be populated in induced nuclear reactions. An energetic ion beam produced by a particle accelerator is focused on to a target of a specific material. When a projectile nucleus hits a target nucleus a Compound nucleus reaction may take place (see schematic view).

Projectile and target nuclei form a rotating highly excited Compound nucleus. This deexcites by emitting protons (p), neutrons (n) or even heavier particles as alpha particles (a). If the excitation energy is no longer sufficient to emit particles, the final nucleus produced after the particle emission continues to deexcite by emitting a spectrum of characteristic g rays (see figure).

A measurement of the properties of these characteristic g rays enables the physicist to construct a scheme of the energy levels, in which the nucleus can exist (see a drawing of a level scheme). From this scheme information about the structure of the excited states can be obtained.

How do we measure g rays?

Energy spectra of g rays and coincidence events (cascades of g rays correlated in time) are measured with solid-state detectors made of high-purity Germanium (HPGe detectors). These detectors are arranged in big sphere-shaped arrays that surround the target and cover a large solid angle. Such gamma spectrometers have been designed and constructed in national or international collaborations:

The European project EUROBALL is supposed to be the world's largest gamma spectrometer at present. Its implementation EUROBALL III was working for two years at the Laboratori Nazionali di Legnaro ( LNL) near Padova, Italy. The photograph shows the opened spectrometer. On the left one can see the vessels for liquid nitrogen of the backward detectors of the left hemisphere. In the middle of the figure the interior of the right hemisphere is visible. It shows the conventional detectors in forward direction (left), the so-called CLOVER detectors mounted on a ring perpendicular to the ion-beam axis (top and bottom) and the so-called CLUSTER detectors at backward direction (right). The ion beam passes the horizontal vacuum tube coming from the right. The target chamber is positioned in the centre of the spectrometer, but is removed in the photograph.

The present implementation EUROBALL IV has recently been set up at the Institute de Recherches Subatomiques ( IReS) in Strasbourg, France. The photograph shows the forward hemisphere of the spectrometer. The rear sides of the vessels for liquid nitrogen mounted to the detectors are visible. They are connected with an automatic filling system via the black tubes. In the centre of the sphere the hole for mounting the vacuum tube of the beam line can be seen.

The spectrometer GAMMASPHERE, presently at the Argonne National Laboratory (ANL) near Chicago, is the american equivalent to EUROBALL. The photograph shows the opened spectrometer. One can see the escape-suppression shields surrounding the Germanium detectors and the collimators in front of the detectors. Behind the spectrometer, in the middle of the photograph, the fragment mass analyzer (FMA) is visible.

The spectrometer GASP is in operation at the Laboratori Nazionali di Legnaro ( LNL) near Padova, Italy. The photograph shows the opened spectrometer. The vacuum tube of the beam line can be seen in the middle of the figure. The Germanium detectors and the smaller Bismuth Germanate detectors of the so-called inner ball of one hemisphereare are visible. The yellow shell is the frame supporting the detectors.

The spectrometer EUROBALL contains 15 so-called CLUSTER detectors. As shown in the schematic view, a CLUSTER detector comprises seven individually encapsulated HPGe crystals of about 60 % efficiency (relative to a 3" X 3" NaI crystal) in a common cryostat surrounded by an escape-suppression shield consisting of 18 optically isolated Bismuthe Germanate (BGO) scintillator crystals. The CLUSTER detector was designed at the Institut für Kernphysik (IKP) der Universität zu Köln and the IKP of the FZ Jülich. Three of the CLUSTER detectors installed in the EUROBALL were assembled at the FZR.

An additional CLUSTER detector was built in the FZR for other purposes. This detector has been used for various experiments such as studies of dipole excitations at the electron accelerator S-DALINAC of the TU Darmstadt and studies of exotic nuclei at the On-Line Mass Separator at the GSI Darmstadt. It is planned to use this detector in future nuclear resonance fluorescence (NRF) experiments at the superconducting electron accelerator ELBE which has been built at the FZR. The photograph shows the CLUSTER during the preparation for NRF experiments at the S-DALINAC. On the left the BGO shield can be seen. The cryostat containing the seven detector capsules is pulled out of the shield along the horizontal rods and is visible on the right of the blue flange. Behind the cryostat, the back part of the BGO shield consisting of six hexagonal detectors with the photomultiplier tubes can be seen. The small boxes behind the next blue flange are the preamplifiers. The big vessel on the right contains liquid nitrogen for cooling the HPGe crystals.

In nuclear-structure experiments one often wants to investigate nuclei which are very weakly populated in the available nuclear reactions. The g rays emitted by these nuclei are very weak and superimposed by g rays arising from other, much stronger populated nuclei. One way to suppress the interfering g rays is to select the particular reaction channel leading to the final nucleus of interest by measuring the emitted particles (protons, neutrons, a particles, ...) in coincidence with the g rays. For this purpose, particle detectors have been developed and installed in the gamma spectrometers. To measure charged particles as protons, a particles etc. the Rossendorf Silicon ball (RoSiB) has been designed and built in the detector laboratory) of our institute. This detector ball has been designed for the use as an ancillary detector for the gamma spectrometer EUROBALL. It consists of 12 pentagonal and 30 hexagonal silicon detectors of 0.5 mm thickness mounted on ceramic backings. In the photograph one can see the white ceramic backings of the detectors, the contacts for the cables and the screws for mounting the individual pieces. A special detector technique in conjunction with special electronics for the signal processing allows a precise particle identification to be made. This technique was applied for this first time in a system like RoSiB. Results of a test experiment (see below) have shown that this method allows a more precise discrimination between different charged particles than conventional techniques.

Recently, a surprising phenomenon has been observed in nearly spherical Pb isotopes around A = 200. While the excited states at low spin show irregular multiplet-like structures as expected for nearly spherical nuclei, regular sequences that follow the J (J+1) rule evolve at high spin, indicating a rotational mode. The levels of these sequences are linked by strong magnetic dipole (M1) transitions whereas cross-over E2 transitions are very weak. These observations contradict the common understanding of nuclear physics, that only well-deformed nuclei should exhibit rotational bands.

A solution of this apparent paradoxon has been given in the framework of the Tilted Axis Cranking (TAC) model developed by S. Frauendorf. The coupling of angular momentum vectors of few high-j nucleons is the basic mechanism for generating the total spin J of the nucleus. Few protons occupy orbitals with long spin vectors above a closed shell (high-j particle-like orbitals) while the neutrons fill up a shell except for few holes (high-j hole-like orbitals), or vice versa.

A perpendicular coupling of their angular momenta is energetically favoured because it maximises the overlap of the spatial density distribution. This coupling results in a substantial component of the magnetic dipole moment, which is transverse to the total spin and gives rise to large M1 transition strengths of several m²_N. This is schematically viewed in the left figure. As the magnetic dipole rotates about the axis of the total angular momentum, this new mode has been called "Magnetic Rotation".

The total angular momentum is increased by the gradual alignment of the individual particle and hole spins along the axis of the total angular momentum. Magnetic rotation manifests in regular rotational bands with strong M1 and very weak E2 transitions as displayed in the right figure. The ratios of the transition strengths are typically in the order of B(M1)/B(E2) ˜ 20 - 40 (m_N/eb)².

The TAC model predicts magnetic rotation in several regions of the nuclear chart (see figure). These regions are characterised by nuclei of low deformation in the vicinity of shell closures. One of the mass regions, where magnetic rotation is predicted to occur, is located around A = 80. To search for the predicted appearance of magnetic rotation in this region, we have investigated the isotopes ⁸²Rb and ⁸⁴Rb, which have 9 proton particles above the Z = 28 shell and 5 or 3 neutron holes in the N = 50 shell, respectively. The experiment was carried out with the spectrometer GASP at the Laboratori Nazionali di Legnaro ( LNL) near Padova, Italy.

On the basis of this experiment we have found M1 bands in both nuclei. For illustration, the figure on the right shows a partial level scheme of ⁸²Rb including the M1 band and its deexcitation to low-lying states. A striking feature of the M1 bands is the regularity of the level spacings [J ˜ hw, hw = E_g(M1)]. This can be seen in the upper panel of the lower figure for the case of ⁸²Rb. The magnetic character of the rotation is demonstrated by the ratios of transition strengths B(M1)/B(E2) for each level in the band. These ratios are shown in the lower panel of the figure. They reach values up to about 20 (m_N/eb)², which are comparable with the ratios in other regions of magnetic rotation. The B(M1)/B(E2) ratios decrease smoothly with increasing rotational frequency hw, manifesting the shears mechanism. Hence, we have found the main characteristics of magnetic rotation. We have interpreted the M1 bands in ⁸²Rb and ⁸⁴Rb in the framework of the TAC model. In the calculations we have assumed the lowest-lying four-quasiparticle configuration for the M1 bands. As can be seen in the figure for ⁸²Rb, the calculated dependence of the spin on the rotational frequency follows well the experimental behaviour. Moreover, the calculated B(M1)/B(E2) ratios are in excellent agreement with the experimental values. This shows the applicability of the concept of magnetic rotation to these bands. It is the first evidence of this novel rotational mode in the mass region around A = 80, as predicted by the TAC model.

Nuclei around the shell closure at the neutron number N = 50 display a diversity of structural phenomena which vary drastically with small changes of the nucleon numbers. The semi-magic nuclei with N = 50 display an irregular multiplet-like structure at low spin. For example, E2 transitions between low-lying states in ⁸⁶Kr and ⁸⁹Y have transition strengths of B(E2) < 5 Weisskopf units (W.u.) indicating a nearly spherical shape of the nucleus. High-spin states in those nuclei are created by few-particle excitations that form multiplets by recoupling the spins of the involved proton and neutron orbitals. This recoupling causes large B(M1) transition strengths. Similar observations have been found for nuclei with one hole in the N = 50 shell as ⁸⁵Kr and ⁸⁶Rb. However, already at N = 48, two neutron holes apart from the closed shell, one observes the onset of collectivity. In our investigations of the N = 48 nuclei ⁸³Br, ⁸⁵Rb and ⁸⁷Y we have observed yrast sequences with regular level spacings and weakly collective E2 transition strengths of B(E2) ˜ 15 W.u. at low spin. We have interpreted these nuclei in the framework of the nuclear shell model. As a remarkable result of the calculations, the weakly collective properties of the yrast states are reproduced in the calculations especially for ⁸³Br and ⁸³Rb, which is illustrated in the following figure.

Here, the numbers at the arrows are E2 transition strengths, while those at the calculated levels are quadrupole moments. It can be seen that our large-scale shell-model calculations reproduce the regular spacings between the lowest three states and the slightly collective E2 strengths. In the calculations these properties result from a coherent superposition of many contributing proton and neutron excitations. This interpretation shows that the microscopic shell model can describe collective phenomena to a certain extent, if the model space is large enough.

At high spin (J > 21/2) the level spacings are irregular. The high-spin states are linked by strong M1 transitions while E2 transitions are not observed. These states may be characterised by particle excitations without any collective motion. This is displayed in the following figure, where the blue numbers at the arrows are B(M1) values in W.u.

The energy levels as well as the M1 transition strengths predicted by the shell model are in good agreement with the experimental quantities. The shell model describes the considered high-spin states as multiplets formed from three-particle excitations (states with 21/2 < J < 25/2) and five-particle excitations (states with 27/2 < J < 33/2). In this description, the large M1 transition strengths arise from a recoupling of the spins of the involved proton and neutron orbitals. This mechanism is an analogue to the alignment of the particle and hole spins generating high-spin states in an M1 band representing magnetic rotation (see above).