Upper Limit ofTNonconservation in the ReactionsMg24+α⇄

Abstract

Time-reversal invariance has been tested via detailed balance in the compound-nuclear reactions 24 Mg+o; ^2 7 Al+p.The relative differential cross sections agree within the experimental uncertainties, leading to an estimated upper limit for the ratio of the Tnonconserving to the T-conserving reaction amplitudes of (2-4) xlO~3. The same upper limit is found for the nuclear matrix elements which are odd with respect to time reversal.Continuing our previous experiments for a search of T-nonconserving effects in compoundnuclear reactions 1 we have studied the reactions 24 Mg + a sr 27 A1 +p under more favorable conditions. We recall briefly the idea of the experiment:A most sensitive test 2 of time-reversal invariance by detailed balance should be provided by a reaction proceeding via a compound nucleus which is excited in the region of strongly overlapping levels. The interference of many coherently excited resonanced then gives rise to statistical fluctuations of the cross section as a function of energy. In the presence of a time-reversal-odd force the reaction amplitude can be split into a T-conserving and a small T-nonconserving part which are assumed to fluctuate independently of each other. 3 This implies that the T-odd part of the amplitude should be enhanced relative to the T-even one at a minimum of the cross section where the time-reversal-even amplitude is reduced. The most favorable case, of course, will be a reaction where only one single spin channel contributes to the cross section. This is true for the two reactions 24 Mg + a^=-27 A1 +p at 0 = 0° and 0 = 180°. The experiment consisted in the measurement of excitation functions at an angle 6 C m =172.6°, where the admixture of further amplitudes was estimated to be less than 10%.The a particles and protons were accelerated by the Heidelberg tandem Van de Graaff. Great effort was made to minimize the background in the spectra. The very carefully prepared targets (15 mm in diameter) consisted of isotopically enriched magnesium (99.96% 24 Mg, 33 jig/cm 2 ) evaporated onto thin carbon foils and of self-supporting aluminum (35 /ig/ cm 2 ), respectively. The a particles were detected with silicon surface-barrier counters, the protons with lithium-drifted silicon counters, both of them cooled to about -40°C. In the (a>p) measurement, 8-and 9-/i-thick aluminum foils were placed in front of the counters in order to shift a particles to the lowenergy end of the spectrum. All other experimental arrangements were the same as in the previous measurements. 1 The cross sections in both reactions were taken at a very high maximum at Ep ~ 10.3 MeV and E a ~ 13.45 MeV and at two other energies, viz. a rather wide minimum at Ep~ 10.55 MeV and E a ~13.73 MeV and a second maximum at E p -11.3 MeV and E a~ 14.6 MeV. In order to avoid the measurement of absolute values, the cross sections of the two reactions were normalized in the high maximum (Fig. 1) and then compared with each other in the minimum and in the second maximum. Since the energy spread in the entrance c...

Scattering experiments with microwave billiards at an exceptional point under broken time-reversal invariance

“…This was possible since both, amplitude and phase of the S-matrix elements, were accessible. In nuclear physics [108][109][110][111][112] only the weaker principle of detailed balance, which is induced by a ferrite that was magnetized by an external magnetic field B. This is to be distinguished from dissipation [54].…”

Cross-section fluctuations in open microwave billiards and quantum graphs: The counting-of-maxima method revisited

“…[21,22] in the context of nuclear physics [3,23,24]. In addition, the effect of time-reversal invariance (T ) violation, which has been tested in nuclear spectra [25] and for the Ericson region in compound-nucleus reactions [26][27][28][29][30][31], is inspected in this regard. From a theoretical perspective, simulations are performed using random matrix theory (RMT) and the Verbaarschot-Weidenmüller-Zirnbauer (VWZ) approach [1], accompanied by a formal appraisal of chaotic scattering on networks of quantum wires [32], so-called quantum graphs, [33][34][35][36][37].…”

Induced Violation of Time-Reversal Invariance in the Regime of Weakly Overlapping Resonances

“…In particular, RMT yields analytical expressions for correlation functions of scattering amplitudes [2] that can be generalized to include T violation. Although widely used (to discover signatures of T violation in compound-nucleus reactions [3] in the Ericson regime [4], to describe electron transport through mesoscopic samples in the presence of a magnetic field [5], and in ultrasound transmission in rotational flows [6]), that generic model for T violation has, to the best of our knowledge, never been exposed to a detailed experimental test. With our data we perform such a test.…”