A cornerstone of physics, Maxwell's theory of electromagnetism, apparently contains a fatal flaw. The standard expressions for the electromagnetic field energy and self-mass of an electron of finite extension do not obey Einstein's famous equation, $E=mc^2$, but instead fulfill this relation with a factor 4/3 on the left-hand side. Many famous physicists have contributed to the debate of this so-called 4/3-problem but without arriving at a complete solution. Here, a comprehensive solution is presented. The problem is caused by an incorrect treatment of rigid-body dynamics. Relativistic effects are important even at low velocities and equivalence between electromagnetic field energy and self-mass of the electron is restored when these effects are included properly. In a description of the translational motion of a rigid body by point-particle dynamics, its mechanical energy and momentum must be defined as a sum of the energies and momenta of its parts for fixed time, not in the laboratory as in the standard expressions but in the rest frame of the body, and for consistency of the description, the energy and momentum of the associated field must be defined in the same way.

"Investigation of the energy and temperature dependence of the string effect" Can. "n-typ dopants and conduction-band electrons in diamond: Cluster molecular-orbital theorie" "Lattice sites of arsenic ions implanted in diamaond" and the ISOLDE-Collaboration " Microscopic studies of implanted 73 As in diamond: γ-e PAC and emission channeling experiments. " Abstract submitted to

We have studied the photo physics of C60(-) anions in the electrostatic storage ring ELISA with ions produced in a plasma source and cooled and bunched in a He filled ion trap. A previous study using delayed electron detachment as a signal of resonance-enhanced multiphoton electron detachment (REMPED) has been repeated both at room temperature and with the trap cooled to liquid nitrogen temperature. However, wavelength dependence of the overlap of the strongly focused laser beam with the ion beam introduces distortions of the absorption spectrum. We have therefore applied a new method, combining the IR light with a slightly delayed, powerful UV pulse (266 nm). After absorption of three UV photons, the ions decay by delayed (thermal) electron emission, and time spectra are recorded for varying wavelength. The fraction of ions heated by absorption of a single IR photon is then extracted from a principal component analysis of these spectra. In good agreement with the earlier REMPED experiment, an origin band for transitions between the two lowest electronic levels of the anion, with t1u and t1g symmetry, is observed at 9380 cm(-1), with strong sidebands from excitation of the two A(g) and eight H(g) vibrations. As before, a hot band is observed at about 9150 cm(-1) and assigned to a transition from an excited vibronic Jahn-Teller state. However, an earlier observed band at higher energy, interpreted as a transition from this excited state to an excited vibronic state in the t1g electronic level, is much weaker in the new measurements and could be an H(g) vibrational sideband. Also earlier studies of direct laser detachment from C60(-) in the storage ring ASTRID have been revisited, with ions cooled by liquid nitrogen in the ion trap. We confirm the previous measurement with a determination of the threshold for s-wave detachment at 2.664 ± 0.005 eV, slightly lower than a recent value of the electron binding, 2.683 ± 0.008 eV, obtained from the energy spectrum of photo electrons. The detachment yield is observed to increase sharply for photon energies above a threshold at 2.78 eV, maybe caused by either Feshbach resonances or a shape resonance due to the presence of a bound electron state in the continuum.

We present a detailed study of the electronic structure and the stability of C(60) dianions in the gas phase. Monoanions were extracted from a plasma source and converted to dianions by electron transfer in a Na vapor cell. The dianions were then stored in an electrostatic ring, and their near-infrared absorption spectrum was measured by observation of laser induced electron detachment. From the time dependence of the detachment after photon absorption, we conclude that the reaction has contributions from both direct electron tunneling to the continuum and vibrationally assisted tunneling after internal conversion. This implies that the height of the Coulomb barrier confining the attached electrons is at least approximately 1.5 eV. For C(60)(2-) ions in solution electron spin resonance measurements have indicated a singlet ground state, and from the similarity of the absorption spectra we conclude that also the ground state of isolated C(60)(2-) ions is singlet. The observed spectrum corresponds to an electronic transition from a t(1u) lowest unoccupied molecular orbital (LUMO) of C(60) to the t(1g) LUMO+1 level. The electronic levels of the dianion are split due to Jahn-Teller coupling to quadrupole deformations of the molecule, and a main absorption band at 10,723 cm(-1) corresponds to a transition between the Jahn-Teller ground states. Also transitions from pseudorotational states with 200 cm(-1) and (probably) 420 cm(-1) excitation are observed. We argue that a very broad absorption band from about 11,500 cm(-1) to 13,500 cm(-1) consists of transitions to so-called cone states, which are Jahn-Teller states on a higher potential-energy surface, stabilized by a pseudorotational angular momentum barrier. A previously observed, high-lying absorption band for C(60)(-) may also be a transition to a cone state.

The cooling rates of C60- have been measured in an electrostatic storage ring between several hundred mus and several tens of ms with one-photon laser excitation. The absolute energy scale is established by the photon energy, and the cooling time interval is derived from the nonexponential decay of the ensemble of hot molecules. The energy decreases due to the combined action of depletion and thermal emission of IR photons with a total energy loss rate that varies inversely proportional to time, 0.9 eV/t. The radiative component decreases from a few hundred eV/s at submillisecond time scales to several tens of eV/s at 20 ms and confirms that the crossover from depletion to predominantly radiative cooling occurs around 5 ms. The method is applicable to any large molecule or cluster which decays spontaneously, irrespective of the specific decay channel.

The time delays in fission induced by bombardment of W with 180 MeV S-32, 240-255 MeV Ti-48, 330-375 MeV Ni-58, and 390 MeV Ge-74 have been measured by observation of crystal blocking. Nearly all results are consistent with exponential decay with lifetimes of order 10(-18) s which depend weakly on the atomic number of the composite nucleus. This is inconsistent with the Bohr-Wheeler model of fission from a compound nucleus in statistical equilibrium at each stage in a neutron evaporation cascade and supports a picture of strongly damped quasifission. A simple diffusion model with one-body dissipation reproduces roughly the observed time scale and the exponential decay. It suggests that the outer fission barrier could play a significant role in the observed, very slow decays.

The time delay in fission induced by bombardment of W with 180 MeV $^{32}\mathrm{S}$, 240--255 MeV $^{48}\mathrm{Ti}$, and 315--375 MeV $^{58}\mathrm{Ni}$ has been measured by observation of crystal blocking. There is a clear narrowing and a small increase in the minimum yield of the angular dips for fission compared with scaled dips for elastically scattered ions. This is interpreted as a fission delay of about 2 as, only weakly dependent on energy and atomic number. The delay is longer by 1 to 2 orders of magnitude than obtained from standard interpretations of measurements of prescission neutrons and giant-dipole-resonance gamma rays and from calculations of the nuclear dynamics in heavy-ion reactions.

The time delay in fission induced by bombardment of W with 180 MeV 32S, 240-255 MeV 48Ti, and 315-375 MeV 58Ni has been measured by observation of crystal blocking. There is a clear narrowing and a small increase in the minimum yield of the angular dips for fission compared with scaled dips for elastically scattered ions. This is interpreted as a fission delay of about 2 as, only weakly dependent on energy and atomic number. The delay is longer by 1 to 2 orders of magnitude than obtained from standard interpretations of measurements of prescission neutrons and giant-dipole-resonance gamma rays and from calculations of the nuclear dynamics in heavy-ion reactions.

We have studied the lifetimes of C-60(2+) and C-70(2-) ions in a storage ring. The dianions were produced by electron attachment to the monoanions in a Na vapour cell. In agreement with earlier studies, we find that C-70(2-) is stable on a time scale of seconds. However, contrary to the results of earlier experiments, we find that C-60(2-) decays on a time scale of milliseconds. The decay is dominated by electron tunnelling through a Coulomb barrier, mainly from thermally populated triplet states about 0.1 eV above the singlet ground state. The electron binding in C-60(2-) is estimated to be - 0.20 eV, and the lifetime of the ground state is then of the order 20 s.

C 60 2 − and C702− dianions have been produced by electrospray of the monoanions and subsequent electron pickup in a Na vapor cell. The dianions were stored in an electrostatic ring and their decay by electron emission was measured up to 1 s after injection. While C702− ions are stable on this time scale, except for a small fraction of the ions which have been excited by gas collisions, most of the C602− ions decay on a millisecond time scale, with a lifetime depending strongly on their internal temperature. The results can be modeled as decay by electron tunneling through a Coulomb barrier, mainly from thermally populated triplet states about 120 meV above a singlet ground state. At times longer than about 100 ms, the absorption of blackbody radiation plays an important role for the decay of initially cold ions. The tunneling rates obtained from the modeling, combined with WKB estimates of the barrier penetration, give a ground-state energy 200±30meV above the energy of the monoanion plus a free electron and a ground-state lifetime of the order of 20 s.

A delayed ionisation experiment has been carried out on laser excited C76 molecules. Ions and electrons are detected in coincidence to distinguish the ionisation of C76 from that of C74 molecules created by the dominant process, emission of C2. From the power-law dependence of the C76+ yield on time we deduce the dissociation energy, Ed=8.2±0.3eV. The relative yield of C74+ is consistent with very similar Arrhenius parameters for C76 and C74, both for ionisation and for C2 emission. With the assumption of a frequency factor for dissociation, Ad=1019s−1, the power of photon emission from neutral C76 is also determined from the experiment. It is consistent with predictions based on oscillator strengths derived from inelastic electron scattering.

Abstract Mossbauer parameters, measured with a resonance counter, have been compared with channeling results on the same samples, for ′119mSn implanted into silicon single crystals. The implantation dose was varied between ∼1014 and ∼1017 atoms/cm2, for target temperatures of 2O°C and 400°C. The channeling results in hot implants show that Sn is embedded substitutionally, and the Mossbauer parameters are nearly dose independent in the range indicated above. Except for a very low-dose implant (∼1013 atoms/cm2) the room-temperature implants lead to complete damage (no channeling dip) and significantly different Mossbauer parameters. Subsequent annealing at 700°C, however, leads to values close to those characteristic of hot implants. The small dose dependence for hot implants, even for doses leading to ∼80% damage, as measured by channeling, indicates that the microscopic ordering is preserved.

C60(2-) and C70(2-) dianions have been produced by electrospray of the monoanions and subsequent electron pickup in a Na vapor cell. The dianions were stored in an electrostatic ring and their decay by electron emission was measured up to 1 s after injection. While C70(2-) ions are stable on this time scale, except for a small fraction of the ions which have been excited by gas collisions, most of the C60(2-) ions decay on a millisecond time scale, with a lifetime depending strongly on their internal temperature. The results can be modeled as decay by electron tunneling through a Coulomb barrier, mainly from thermally populated triplet states about 120 meV above a singlet ground state. At times longer than about 100 ms, the absorption of blackbody radiation plays an important role for the decay of initially cold ions. The tunneling rates obtained from the modeling, combined with WKB estimates of the barrier penetration, give a ground-state energy 200+/-30 meV above the energy of the monoanion plus a free electron and a ground-state lifetime of the order of 20 s.

We have measured the near-infrared absorption spectrum for isolated C-60(-) ions at room temperature. Two bands, at 9145 cm(-1) and 10460 cm(-1), have been identified in addition to the main absorption band at 9382 cm(-1), seen also at low temperature in a matrix. An interpretation based on the theory of dynamic Jahn-Teller effects is proposed.