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In this paper I develop a new recipe for solving the problem of religious disagreement suggested by the injunction to cultivate intellectual humility conjoined with awareness of human immaturity in deep time. The ingredients brought to the table include such things as noticing the full breadth and texture of the religious propositional field, observing the previously hidden areas of agreement this exposes, making a differential judgment of importance in relation to religious propositions, applying the concept of a position, and finding a better home for an emphasis on detailed beliefs than contexts of inquiry can provide. Special attention is given to the modesty of the proposal, which asks relatively little of religious practitioners while reconceiving this area of discussion.

This is an invited response to Peter Forrest’s review of my trilogy on the philosophy of religion, which appeared in a previous issue of this journal.

In this brief reply I argue that criticisms of the hiddenness argument recently published in this journal by Imran Aijaz and Markus Weidler are without force. As will be shown, their critique of my conceptual version of the argument misses the mark by missing crucial distinctions. Their critique of my analogical version of the argument misunderstands that argument and also misapplies the work of W. H. Vanstone. And their critique of my view that belief is necessary for a certain kind of relationship with God overlooks both some central features of that kind of relationship and some good reasons for not accepting acceptance or anything similarly nonbelieving as a substitute for belief in this context.

This paper criticizes the assumption,omnipresent in contemporary philosophy ofreligion, that a perfectly good and loving Godwould wish to confer on (at least some) finitepersons free will. An alternative mode ofDivine-human relationship is introduced andshown to be as conducive to the realization ofvalue as one involving free will.Certain implications of this result are thenrevealed, to wit, that the theist’s free willdefence against the problem of evil isunsuccessful, and what is more, that free will,if it exists, provides positive support foratheism.

The transfer reaction of negative muons from muonic protium to 3 and 4 in binary and triple gas mixtures was studied. In the binary mixtures the transfer rates to the two helium isotopes were determined from the time distribution of the 7-keV X-rays of the intermediate muonic molecule (pµHe)*. The experimental transfer rate to 4 is in good agreement with theoretical predictions, whereas the rate to 3 is a factor 2 to 3 smaller than the predicted ones. Radiative branching ratios of the (pµHe)8 molecular decay were obtained. Muon transfer from excited states of muonic protium gives the main contribution to the total intensity of the µHe Lyman series in the binary mixtures. Values of q 1s He are determined.

The scientific program and the experimental setup of the DEAR (DAΦNE Exotic Atom Research) experiment at the new φ-factory DAΦNE of Laboratori Nazionali di Frascati are described. The objective of DEAR is to perform a 1% measurement of the K α line shift due to the strong interaction in kaonic hydrogen. A measurement will also be performed on kaonic deuterium for the first time. The aim is to investigate low-energy $$\overline K N$$ physics and to understand SU(3) chiral symmetry breaking. The setup takes advantage of the unique features of the “kaon beam” from the φ decay in DAΦNE; of a low-temperature pressurized gaseous target; and of a detector for soft X-rays – the Charge-Coupled Device (CCD) – characterized by a very good energy (and spatial) resolution and by an unprecedented background rejection capability. The DEAR experiment represents a major effort in the study of low energy $$\overline K N$$ interactions and has the potential to produce a breakthrough in the field.

The energy and time distributions of the decay X-rays of excited, metastable, molecular (dµHe)*-resonances were measured. The comparison of the observed energy spectra with calculated ones suggests that decay from the rotational state J = 1 dominates at the investigated conditions. The muon transfer rates from ground state deuterium to the helium isotopes 3He and 4He at low temperatures were determined from the time distributions of these spectra. Additionally, the temperature dependence of the muon transfer rate was clearly established in deuterium / 4He mixtures.

The DEAR (DAΦNE Exotic Atom Research) experiment at the new φ-factory DAΦNE of Laboratori Nazionali di Frascati aims for a 1% measurement of the line shift of the K-complex due to strong interaction in kaonic hydrogen. This presentation is meant to prove that the high statistics and good resolution obtainable with DEAR will be able to disentangle the kaonic hydrogen K-complex lines (a cascade unconstrained fit), obtaining in this way constraints for what concerns the cascade parameters and, consequently, information regarding the physical processes involved in the kaonic hydrogen atomic cascade.

The present status of research of muon transfer from the ground state of muonic protium to 4He is reviewed. The analysis of a recent measurement in a triple gas mixture of H2+4He+Ne at 15 bar and room temperature is presented and the result is compared to the existing experimental and theoretical rates. The average muon transfer rate from protium to 4He determined from all lifetime measurements is .

The charge exchange reaction of negative muons from the \((\mu {\text{p}})_{1{\text{s}}} \) atom to oxygen has been measured in gaseous mixtures of H2 + O2. The measurements were performed at three different relative oxygen concentrations ranging from 0.2% to 0.8% and total pressures 3.5–15 bar. A mean transfer rate of \(\lambda _{{\text{pO}}}^{\text{t}} = 0.85(2) \times 10^{11} {\text{s}}^{{\text{ - 1}}} \), describing the transfer from the ground state of thermalized \(\mu {\text{p}} \) atoms to oxygen, was determined. In order to investigate the energy dependence of the transfer rate, Monte Carlo simulations of the \((\mu {\text{p}})_{1{\text{s}}} \) thermalization and the muon transfer were carried out. The comparison of measured and simulated time spectra yielded an epithermal transfer rate \(\lambda _{{\text{pO}}}^{\text{e}} \)=3.9 \(\times \) 1011 s-1 in the energy interval 0.12–0.22 eV. The analysis with the model of “Two components” shows that all measured time spectra can be reproduced with the same set of parameters.

The yields of muonic x rays of the Lyman series of nitrogen, neon and argon have been analysed to determine capture ratios A(Z1,Z2) in about thirty gaseous mixtures under different experimental conditions. In addition, capture ratios A(Z,H) have been determined in hydrogen mixtures by taking into account transfer processes from muonic hydrogen to elements Z. The influence of the spectral flux density of the muons on capture ratios has been analysed. Our per-atom ratios form a coherent set and confirm the value A(Ar,Ne) = 1. 262(10).

Several experiments performed by our group in recent years have put into evidence the complex structure of the time distributions of the muonic X-rays following transfer from muonic hydrogen isotopes to heavier elements. Simulations have shown that a substantial fraction of the µp atoms in the ground state have epithermal energies. Therefore, an energy dependence of the transfer rate seems a reasonable assumption for the explanation of the complex time structure.

Muon transfer from hydrogen isotopes to helium is of importance in muon-catalyzed fusion and serves as a unique tool for the direct observation of the mesomolecular ion (pµHe)*. During two data-taking runs in 1994 and 1995 at PSI, measurements of the transfer from protium to helium were carried out using CCD's and Ge-diodes as independent X-ray detectors to obtain information on the time distribution and intensity of the 7 keV decay X-ray of the mesomolecular ion. Dual1H2 +4 He and triple1H2 + Ne +3,4He gas mixtures at low temperatures were investigated to extract transfer rates. Protium of high purity was available. For the first time a transfer rate from muonic protium to3He was measured. A general survey of our measurements and preliminary analysis is presented.

To investigate the energy dependence of muon transfer to oxygen, we performed measurements in gaseous mixtures of hydrogen and oxygen. The time distributions of the muonic oxygen X-rays showed the same structure as the one observed earlier in H2+SO2 mixtures. In the delayed part of these distributions, one can distinguish a short-time and a long-time component. From the latter, we deduced the transfer rates from thermalized muonic protium, respectively deuterium, to oxygen. The short-time component can be interpreted as being due to muon transfer from epithermal muonic hydrogen atoms. The time parameters are characteristic for the deceleration process as well as for energy-dependent transfer rates. With results of recent research on the formation and the thermalization of muonic hydrogen, we performed Monte Carlo simulations in order to test the hypothesis of an energy-dependent transfer rate.

L'A. aborde le probleme du mal d'une maniere logique pour arriver a une conclusion contraire a celle qui est traditionnellement assumee par la philosophie de la religion. Il y a selon lui, une forme hybride de l'argument du mal qui trouve son origine dans des considerations de probabilite, mais qui d'autre part, procede de maniere deductive

The experimental muon transfer rates from muonic protium and deuterium to heavier elements show a complexZ dependence. Instead of the expected monotonicZ dependence considerable variations between neighboring elements are observed. Transfer to neon has a specially small rate. Furthermore, the time distribution of the muonic X-rays shows in a number of molecules a complex structure, and depends in the case of a H2 + CH4 gas mixture also on the total pressure.

A set of experiments is reviewed which makes use of the emission of muonic deuterium from the surface of a layer of solid hydrogen. The behaviour of muons in a solid target system has been studied via detection of muon decay electrons, muonic X-rays, and fusion products (neutrons and charged particles). The emission of muonic deuterium is understood to result from the Ramsauer-Townsend scattering minimum. The energy distribution of the emitted atoms ranges from tenths of eV to about 10 eV, and can be controlled to some extent. A proposal is described to use muonic tritium emission to measure the energy dependence of muonic molecular formation.

After the feasibility of vacuum isolated μ−d production was demonstrated at TRIUMF in 1989, development was begun on a target system that would take advantage of the process to aid in the understanding of the muon catalyzed fusion cycle. Minimal neutron backgrounds, the ability to use silicon detectors, and compatibility with tritium were considered important for a very versatile target system. The advantages which the target gives in isolating μCF process will be outlined.

A study of muonic238U has been performed in a combined (μ−,γ f) and (μ−,γγ) coincidence experiment to investigate the role of non-radiative transitions and their fission probabilities. An augmentation of the outer fission barrier ofΔEb=(0.6±0.1) MeV due to the presence of the muon is deduced. A significant contribution to the prompt fission yield not only results from the (2p→1s) and (3d→1s) non-radiative transitions, but also from other radiationless transitions. Specifically, the measured fission probabilities of the transitions (2p→1s), (3d→1s), and (3p→1s) are (1.5±0.4)%, (5.7±1.7)%, and (5.3±1.9)%, respectively.

Fission fragments from the reaction237Np(μ−,γ,f) have been measured in coincidence with muonic X-rays. The efficiency of the fission fragment detector is determined from (μ−,γ,f)-data of the same experiment. The total fission probability perμ-stopPt has been measured as well as the fission probabilities Pf of the non-radiative muonic (3d→1s)- and (2p→1s)-transitions; the latter has been divided into two parts leading to different mean excitation energiesE:P t =(54±17)%,P f (3d→1s)=(41±21)%,P f (2p→1s,E=6.218 MeV)=(61±19)%, andP f (2p→1s,E=6.525 MeV)=(57±18)%. The influence of the muon on the fission barrier is discussed. The fission probability after muon capture is compared with a calculated value using a distribution of nuclear excitation energies following muon capture and the fission probability as measured in a238U(3He,αf)-reaction.

The probabilities for non-radiative (n.r.) excitationsP n.r. in the muonic nuclides208Pb,232Th, and238U have been determined from (μ−,γγ)-measurements by comparing the intensities of muonic X-ray transitions in single and coincidence spectra. The value ofP n.r. (3p→1s), measured for the first time, is about 90% for the actinides232Th and238U, but only about 8% for208Pb. The value ofP n.r. (3d→1s) is found to be 10 % for233Th, 13% for238U, and about 4% for208Pb. For208Pb a vanishing strength of the n.r. decay of the 2p-level is found, while for232Th and for238U n.r. strengths of about 20% and 26%, respectively, are observed. By regarding two subcomplexes of the 2p→1s transitions leading to different mean excitation energies the n.r. transition probabilities were found to be different for238U only, 21.6% and 31.1.%, respectively.

The time spectra for muon induced fission of233U,234U,235U,236U,238U, and237Np were measured simultaneously, detecting both fragments in coincidence in a fast multi parallel plate avalanche detector. The observed mean lifetimes τ are 68.9 ± 0.3 ns, 70.6 ± 0.2 ns, 72.2 ±0.2 ns, 74.3 ± 0.3 ns, 77.0 ±0.4 ns, and 69.8 ±0.2 ns for the above isotopes, respectively. No second time component, tentatively ascribed to a possible fission isomer, was observed. The deduced total capture rates are compared with theoretical predictions.

In the spectrum of muonic X-rays of238U measured in coincidence with prompt fission events a structure has been found which is attributed to 2p→1s transitions of the muon attached to heavy fragments. The intensityI s of this structure relative to the strengthI pf observed for prompt fission has been determined to beI s/I pf=(6.0± 2.1) %. Although the experimental significance for the appeareance of this phenomenon is weak, this is the first experimental indication for its occuxence.