Quantum Tunneling Study

1. Background

Quantum mechanical tunneling through potential barriers is a widespread phenomenon in natural science, with scope beyond physics and certainly not confined to the decay of radioactive nuclei. Its experimental study is therefore of far-reaching importance in biological sciences, atomic and solid state physics and nuclear astrophysics.

The effect is usually first encountered in the context of alpha decay and the nucleus has been seen as a suitable laboratory to study the phenomenon. Alpha particle angular distributions from sources polarised by low temperature hyperfine interaction methods have been carried out for many years [2]. Recent measurements of alpha decay from oriented nuclei have shown clearly that quantum tunneling through the Coulomb barrier is not generally the dominant factor in determining the angular distribution of alpha emission. Rather the ‘preformation’ of the alpha particle within the nucleus plays a strong role in setting the amplitudes of the angular momentum of partial waves which describe the emission. These nuclear structure effects mean that alpha decay is not a ‘clean’ laboratory for the study of angular momentum dependence in spherical and deformed barrier penetration, although of interest for its own sake [3].

The relatively recently explored processes of proton and neutron emission offer simpler 'cleaner' methods to investigate quantum barrier tunneling since for them there is no 'preformation' question. Furthermore their differing mass and charge means that whilst alpha-decay tunneling is dominated by the Coulomb barrier, proton emission is much more effected by the centrifugal barrier. For example, for 130Nd the proton Coulomb barrier is 14.4 MeV and the centrifugal barrier 3.4 MeV for a partial wave with angular momentum L=2, whilst for alphas the equivalent values are 28.8 MeV and 0.86 MeV. Obviously there is no Coulomb barrier for neutron emission in which the tunneling process is solely determined by the centrifugal barrier.

Experimentally, most cases of direct particle emission are not open to the low temperature polarisation methods of this proposal as they do not live long enough to be cooled to the necessary millikelvin temperatures (but see below). However the related processes, beta-delayed particle emission, allow for polarisation of a longer-lived 'precursor' isotope which beta-decays to excited states in an 'emitter' isotope, which are also polarised, and these excited states emit protons/neutrons in feeding states in a 'daughter'. Beta-delayed emission forms the core of the proposal.

Experiments on beta-delayed protons and neutrons [4] studying properties of highly excited particle emitting states, were pursued in the 1970's and 1980's. They were followed by extensive activity in investigation of ground state, direct, proton radioactivity, mapping the borders of nuclear stability with respect to one-proton decay. This effort, initiated by the Edinburgh group in Daresbury in 1980's and later carried on at Argonne and Oak Ridge National Laboratories, yielded a substantial body of data for both spherical and deformed proton emitters [5]. However, when, as hitherto, the emission is observed from a randomly oriented sample, the only observables carrying fingerprints of the tunneling process are the life-time of the particle-decaying state and the energy spectrum of the emitting particles. Both of these data are dependent indirectly on the angular momentum make-up of the emitted wave.

The vital piece of information still missing is direct measurement of the angular momentum properties of the emission process through the angular distribution of the emitting particles with respect to orientation axis of the proton emitting state. It is the aim of this proposal to provide this essential information for the first time for a range of (beta-delayed) proton and neutron emitters and one case of a direct proton-emitting nucleus. Such experiments are entirely new and provide an exciting new window for the study of quantum tunnelling.


2. Methodology

2.1. Beta-delayed proton emission

In the planned beta-delayed protonexperiments at the NICOLE facility, ISOLDE, CERN, the 'precursor' isotope is produced, mass separated and implanted at 60 keV into a pure ferromagnetic metal foil held at close to 15 millikelvin (mK). The 'precursor' nuclei are then oriented by magnetic hyperfine interaction and decay by (predominantly) allowed Gamow-Teller beta decay to feed, in part, high energy excited states in the 'emitter' isotope. These states may either gamma decay, or emit a proton to reach a state in the 'daughter' final nucleus. The complete beta-delayed particle emission therefore involves the following features:

- 'precursor ' orientation mechanism - transferred directly to 'emitter' states

- beta+ + EC decay

- model description of the excited 'emitter' states in terms of level density models for overlapping or narrowly spaced states or in terms of an appropriate nuclear model for an isolated level

- branching ratio of proton to competing gamma emission probability

- proton transmission coefficients dependent directly on the height and shape of the coulomb/centrifugal barrier

- branching of the proton feeding to different 'daughter' final states

- model for the phase relation between all partial wave components, allowed by angular momentum and parity selection rules, in a proton transition between a given initial and final state.

We note that although beta-delayed proton emission has the same barrier penetration properties as direct proton emission, a second feature of the beta-delayed proton spectrum allows simpler, more direct study of the barrier penetration phenomenon as compared with direct proton emission anisotropy studies. In direct proton decay, as in alpha decay, a single transition is observed between specific nuclear states. For this transition, not only the relative amplitudes of the different partial waves determine the angular distribution, but also their relative phase, 0 or , has strong influence wherever more than one partial wave can contribute - although this is not common. By contrast, in the beta-delayed proton spectrum from medium and heavy nuclei, one is dealing with many unresolved transitions making up the continuous spectrum, originating from levels at energies of order 4-7 MeV in the emitting nucleus. At such high energies there are many states of each spin per 100 keV. Interference effects on the angular distribution may be positive or negative with respect to pure L-waves. However, when many contributions, with differing partial wave amplitude ratios and either phase, are summed, the effect of interference is lost and the result is simply the weighted intensity sum of the contributing partial waves. Thus beta-delayed proton measurements reveal partial wave contributions without the sensitivity, but also without the added complexity, of phase considerations. The relative L-wave intensities determine the proton angular distribution and can be extracted from the sign. magnitude and particle energy and angular dependence of the changes in the observed spectra from the polarised emitter nuclei.

We have explored beta-delayed proton and neutron emission theoretically in detail, building on theory of the process for randomly oriented precursors [6,7] with coverage of the angular distribution properties examining the dependence of the energy spectra and angular distribution upon all variables involved. The resulting computer code to make detailed predictions for individual cases includes allowance for up to 4 final states in the daughter nucleus and a full range of angular momentum waves. This has not previously been done and will be published in the near. Allowed Gamow-Teller beta decay is assumed and the optical model is used to calculate particle transmission coefficients, at present only for a spherical barrier. Ellipsoidally deformed barrier calculations are discussed with our theoretical collaborators.

The experiments are designed to probe the following questions:

1. Basic:

   Are the average sign and magnitude of the spatial anisotropy of the proton angular in agreement with theory?

2. Specific to barrier penetration process and level distribution in the emitter:

   Does the anisotropy of angular distribution vary as predicted with proton energy?

3. By experimenting on a series of systems with differing nuclear deformation:

   Does the anisotropy vary with nuclear deformation (departure from spherical shape) as predicted by barrier penetration theory?


2.2. Beta-delayed neutron emission

Description of this process is very similar to its proton equivalent, with the exception that only the centrifugal barrier is present and thus the neutron spectra extend from energy zero. The experimental programme at the OSIRIS facility, Studsvik, will address the same three questions listed above, but with several differences as now outlined.

Since neutron emission does not need to overcome a Coulomb barrier, in some cases neutrons are emitted from states in the emitter at lower excitation energy. This makes the random phase assumption detailed above for proton emission from medium and heavy nuclei less certain in the case of neutrons. Any remaining phase information will be revealed by additional fluctuating (as opposed to smoothly varying) energy dependence of the neutron angular distribution. Establishing the energy region at which such interference effects are observed is a side result of this work, useful in modeling nuclear excited state densities.

Neutron detection will be made first using 3He and BF3 gas filled detectors, available at Studsvik these have relatively high detection efficiency (~5%) but no energy resolution. Our prediction of anisotropy of the neutron angular distribution from the first planned sample, 137I, shows little variation with energy, so lack of resolution does not impair the ability to address question 1 (above). For later experiments, we will use less efficient (~ 5 x 10-4) detectors which have good energy resolution, thereby gaining access also to question 2. The isotopes chosen once again represent differing emitter deformation (question 3) and all can be strongly oriented after implantation into iron foils at ~15 mK.


2.3. Direct proton emission

Observation of the angular distribution of direct proton emission is more difficult experimentally since direct proton emitter half-lives are generally shorter than the shortest cooling times (of order ms) required to produce on-line cryogenic oriented nuclei. However, certain interesting examples exist of slower direct proton emission. In all cases the longer lifetime of the parent nucleus is thought to arise from hindrance factors in the barrier penetration caused by high angular momentum. As an example of these we cite the case of 147Tm [9] for which we propose to make direct measurement during the grant period as a first direct check on the modeled mechanism of delay.

The half life of the high spin isomer of 147Tm is 580(70) ms [9], comfortably long enough to allow orientation in the enormous [340T] hyperfine field existing at thulium nuclei implanted into iron (the estimated cool down time is less than 20 ms). The emitted proton energy is only just above 1 MeV, which, along with a difference of 5 units in angular momentum, predicted by model calculations, between emitter and daughter states, is thought to be the reason for the slow decay [9]. The proposed experiment will establish directly the angular momentum of the emitted proton wave to the 0+ ground state of 146Er. From the L value, the spin of the 147Tm high-spin isomer, currently only model based and not obtainable from half-life or proton energy directly, are determined uniquely.

Theoretical description of the angular distribution of direct proton emission is done along the same lines as for the beta-delayed emission. It is of course very much simplified as only the mechanism of orientation of the proton emitter and proton transmission coefficients are needed for description of the emission process. For emission to 0+ ground states and hence unique L value, barrier transmission is NOT a parameter in the angular distribution, but, as detailed for 147Tm, the experiment yields the spin of the emitter independent of any model assumptions.

2.4. Exploitation of the Oxford nuclear orientation facility

The Oxford facility is essential for setting up and testing all technical developments before taking them abroad and for training students whilst doing experiments on longer lived isotopes. A particular idea we will develop addresses the problem that the emitted particle spectra are continuous and feeds to different daughter states are not separated. We intend to use 'gamma tagging' to identify those emitted particles which feed one state by requiring coincidence between a gamma transition known to de-excite the state and the incoming particle. This will give a more detailed measurement, but the cost in reduced count rate is high as at the refrigerator gamma detectors are relatively far from the source. We have pioneered the use of this 'gamma tagging' method to study individual beta transitions in complex beta spectra and will explore its application to the weaker particle emission process [10].

Also at Oxford we run a unique PrNi5 cooling system which is the only nuclear orientation facility in the world capable of cooling radioactive isotopes to below 1 mK - an order of magnitude lower than at the on-line facilities. This system will continue to be used, as in the past, with longer lived isotopes to establish precise values of parameters of orientation (e.g. hyperfine fields) which are then used for on-line work with shorter lived isotopes of the same element. Development of the PrNi5 system for on-line use is planned.



[1] J.Rikovska and N.J.Stone, in Proton Emitting Nuclei, AIP 518 , 2000, p.316

[2] D.L.Hill and J.A.Wheeler, Phys.Rev. 89 (1953) 1102.

[3] P.Schuurmans et al. Phys.Rev.Letters, 77 (1996) 4720.

[4] Chs. 4 and 6 in Particle Emission from Nuclei, eds D.N.Poenaru and M.S.Ivascu, CRC press, 1998.

[5] P.J.Woods and C.N.Davids, Ann Rev. Nucl. Part. Sci. 47 (1997) 541.

[6] P.Hornshoj et al., Nucl. Phys. A187 (1972) 609.

[7] A.C.Pappas and T.Sverdrup, Nucl. Phys. A188 (1972) 48.

[8] B.D.D.Singleton et al., Hyp. Int. 75 (1992) 471.

[9] P.J.Sellin et al., Phys. Rev. C47 (1993) 1933.

[10] T.Giles et al., Hyp. Int. 120/121 (1999) 667.