Physics Reports 354 (2001) 243–409 The nuclear physics of muon capture D.F. Measday ∗ University of British Columbia, 6224 Agricultural Rd., Vancouver, BC, Canada V6T 1Z1 Received December 2000; editor: G:E: Brown Contents 4.8. Charged particles 330 4.9. Fission 335 1. Introduction 245 5. -ray studies 343 1.1. Prologue 245 5.1. Introduction 343 1.2. General introduction 245 5.2. Silicon-28 350 1.3. Previous reviews 247 5.3. Lithium, beryllium and boron 360 2. Fundamental concepts 248 5.4. Carbon, nitrogen and oxygen 363 2.1. Properties of the muon and neutrino 248 5.5. Fluorine and neon 372 2.2. Weak interactions 253 5.6. Sodium, magnesium, aluminium, 372 3. Muonic atom 264 phosphorus 3.1. Atomic capture 264 5.7. Sulphur, chlorine, and potassium 377 3.2. Muonic cascade 269 5.8. Calcium 379 3.3. Hyperÿne transition 275 5.9. Heavy elements 383 4. Muon capture in nuclei 281 6. Other topics 387 4.1. Hydrogen 282 6.1. Radiative muon capture 387 4.2. Deuterium and tritium 284 6.2. Summary of g determinations 391 4.3. Helium-3 290 P 6.3. The (; e±) reaction 393 4.4. Helium-4 294 7. Summary 395 4.5. Total capture rate 294 Acknowledgements 396 4.6. General features in nuclei 300 References 397 4.7. Neutron production 311 ∗ Tel.: +1-604-822-5098; fax: +1-604-822-5098. E-mail address: [email protected] (D.F. Measday). 0370-1573/01/$ - see front matter c 2001 Published by Elsevier Science B.V. PII: S 0370-1573(01)00012-6 244 D.F. Measday / Physics Reports 354 (2001) 243–409 Abstract We review the topic of muon capture in nuclei and show that signiÿcant nuclear physics is being learnt from recent experiments. The focus of many earlier experiments had been the particle physics and weak interactions aspects of the subject. Although these were useful conÿrmation of basic ideas, deÿning experiments mostly came from other areas. Thus, we focus on what can be learnt about nuclei especially 1+,1− and 2− magnetic transitions. Valuable comparisons can be made to other charge exchange reactions such as (−;), (−;0), (n; p), (d; 2 He) and (t; 3 He). However, all those experiments have resolutions of 300 keV to 1 MeV, or even worse, so -ray studies of muon capture provide resolutions 100–1000 times better, and thus deÿne the levels unambiguously. For even–even nuclei one can also compare to (e; e)at180◦,or(p; p) at forward angles, for which the resolution is reasonable, typically 50–100 keV, but isospin mixing complicates the comparison. With the recent substantial progress in Shell Model calculations, we anticipate signiÿcant developments in our understanding of nuclear structure in the next few years. c 2001 Published by Elsevier Science B.V. PACS: 23.40.Hc D.F. Measday / Physics Reports 354 (2001) 243–409 245 1. Introduction 1.1. Prologue Muon capture in nuclei has been a secluded garden slightly oC the main tourist routes of particle and nuclear physics. Few major discoveries have been made there, but it has often been a refuge where one could admire the beauty of nature and verify the ideas which were created elsewhere. The weak interaction has been a fertile zone of sub-atomic physics. Many major discoveries have been made therein and these are the foundation of many of our paradigms of particle physics such as “The Standard Model”. Muon physics has been a major part of that development, and muon capture in nuclei a useful adjunct. The ÿeld grew upon the research at the old synchrocyclotrons in the 1950s and 1960s and most of the basic concepts date from that era. There was a second coming at the meson factories in the 1980s and 1990s; improved equip- ment resolved many old problems although many remain. We postulate that these unresolved problems are due to the complexity of the nuclear environment and not due to an imperfect understanding of the weak interactions. Thus, we can now turn this around to use muon capture as an excellent test of our understanding of complex nuclei. With the recent improvement in calculational technology for the shell model in quite heavy nuclei, there is a very real hope that signiÿcant improvement in our knowledge will emerge. There are many existing reviews on muon capture but almost all written from the point of view of a theorist. This perspective is very valuable, but much information which is relevant to an experiment is omitted from such an approach. An obvious example is the subject of muonic X-rays which for a theorist is legitimately considered another topic. In an experiment however, muonic X-rays are both a curse and a blessing, but certainly cannot be ignored. Thus this review is written for those who may pursue such muon capture experiments in the future. We shall show that we now know what were the problems with previous experiments. To overcome these diIculties will take resources which may become available in new facilities such as the Joint Project for High Intensity Proton Accelerators at Tokai, Japan. 1.2. General introduction Ever since its discovery in 1937, the muon has been an enigma which has fascinated and frustrated physicists of several generations (not only the second). We shall take the point of view that the general properties of the muon have been established in particle experiments and that any new discoveries, as important as they will be, will not substantially aCect the problems addressed in muon capture. We shall also assume that lepton universality holds better than we need, so that the many lessons learned from ÿ decay can be transferred over to muon capture which thus can be considered as an extension of electron capture, though with many more states available. Muon capture centres on the simple semi-leptonic reaction − + p → n + ; (1.1) 246 D.F. Measday / Physics Reports 354 (2001) 243–409 which occurs via the charged current of the weak interactions. A feature which turns out to be critical is the extreme spin sensitivity of this reaction for p atoms in the 1s state. The singlet capture rate is about 660 s−1 whereas the triplet rate is only 12 s−1 or so. Many experiments performed at the old synchrocyclotrons showed that these capture rates for hydrogen are roughly correct, but the experiments are hard, and complicated by the fact that absorption actually takes place from a pp molecule. Recently, however, a remarkably precise experiment has been reported on the reaction − 3 3 + He → + H : (1.2) A rate of 1496 ± 4 s−1 was measured and this is in agreement with theoretical estimates for a statistical mixture of the hyperÿne states. We shall therefore assume that the particle physics aspects are well understood. When a muon reaches the 1s state of a muonic atom, it can decay or be captured on a bound proton. Except for very light nuclei this capture is far more likely than decay and it is the general features of this capture which will be the focus on this review. We shall show that the many characteristics which are poorly understood are reKections of the complexity of the nuclear environment. This manifests itself in two ways, either the renormalization of the coupling constants, or the complications of nuclear structure. Great strides are being made in understanding both aspects and we shall see that further developments are just around the corner. When muon capture occurs in any nucleus, the energy release of about 100 MeV is mainly donated to the neutrino, but the nucleus can and does absorb substantial energy, thus many reactions occur. Let us take 28Si as an example because we shall see that many experiments have focussed on this nuclide. First remember that in the 1s state of muonic silicon, the muon will decay 34% of the time and capture on the nucleus 66% of the time. Of those captures, about 36% will produce no neutrons, 49% will produce 1 neutron, 14% will produce 2 neutrons and 1% will produce 3 neutrons. Thus, symbolically: − 28 28 ∗ + Si → Al + : (1.3) Since an excitation of at least 21 MeV is required to produce 2 neutrons, we can see that the nucleus receives more than one might have expected. As a guide one should remember that, for muon capture from a p atom, the recoiling neutron takes only 5.2 MeV of kinetic energy, whilst the neutrino takes away 99.1 MeV. Most experiments have concentrated on the small fraction of reactions that leaves the ÿnal nucleus in a bound state. In this example 28Al is bound up to 7.7 MeV leaving over a hundred levels able to be excited. Fortunately, there are only a chosen few. It is known that 26% of the captures produce bound states of 28Al. (The diCerence between this number and the 36% above is that “no neutrons” includes a proton or an alpha being ejected from the nucleus.) The bound state transitions can be observed via their -ray emission, but only 16% of muon captures in 28Si have been identiÿed as going to 28Al bound states, i.e., about half of the expected number. This is typical of such comparisons for most nuclei, and we now realize that the other transitions are actually there, but just hidden in the overwhelming background. These other transitions often produce high energy -rays which are Doppler broadened, and the eIciency of the HPGe detector is much lower, so more experimental time is required. Modern experiments with larger, more eIcient detectors, could thus study the topic more D.F.