Question 2 You have no electrons in the "2s" orbital, which is between the "1s" and "2p" levels. Question 3 You have two electrons in one "2p" orbital, but none in the other "2p" orbitals.
Question 4 The electrons in the half-filled "4d" orbitals don't all have the same spin. Question 5 You filled the "4d" orbitals before you filled the "4p" orbitals, which are lower in energy. This violates the Aufbau Principle.
Related questions How do electron configurations in the same group compare? How do the electron configurations of transition metals differ from those of other elements? How do electron configurations affect properties and trends of a compound? What is the electron configuration for a sodium ion?
What is the electron configuration for a nitride ion? What is the electron configuration of chromium? What is the electron configuration of copper? What is Hund's Rule? What is the ground state electron configuration of the element germanium? The number of the candidate PEP violating events is obtained from the second step of the simultaneous fit, the result of which is plotted in Fig.
We summarize the free parameters in the second step of the fit in Table 1. The continuous background is described with a first order polynomial function. As the two data sets were taken under the same background conditions, which should lead to identical shape represented by the slope of the first order polynomial background, we introduced a common pol 1 parameter for spectra both with and without current.
Then we used two independent pol 0 parameters to represent the different background levels of the two spectra due to the difference in exposure time.
The ratio between these two intensities from the fit is consistent with the ratio of exposure times. In this way the statistics of the two spectra was used as it is without normalization using the exposure time, and any effect from the uncertainty of the exposure time is included in the fit error of the PEP violating component amplitude, which is the only physics parameter of the fit.
The Fano factor and the Constant Noise that describe the energy-dependent resolution are also free parameters, and the energy resolutions obtained from the two steps of the fit were confirmed to be consistent in eV FWHM at 8. Note that the copper fluorescence X-rays are the background for our candidate event, and they originate from the copper when irradiated by the gamma background in the barrack or the cosmic rays.
We also included the K -series lines from nickel in the fit as we confirmed the existence of this component from data taken in the first half of with three times the statistics. However we cannot yet identify the exact origin of the nickel inside the setup. It will be one of the studies to be carried out in the future. Compared with the method of subtracting the spectra with and without current, which has been used in previous publications where the same experimental method was used, the simultaneous fit has the following differences and advantages:.
This procedure introduces a systematic error that could not be precisely assigned. The simultaneous fit on the other hand does not need a normalization to the histograms, since the intensities of the fluorescence lines and the continuous background are free parameters in the fit.
In the subtraction method, events are counted in one bin, and the statistical error of the count is derived assuming a Poisson distribution for the number of events. However, the simultaneous fit does not require the definition of ROI, since a wide energy range of the spectra is considered in determining the parameters of the global function, from the result of which the number of candidate PEP violating events is obtained.
These uncertainties are usually not evaluated when using the subtraction between the signal and background spectra. Additionally, the present method also returns correlations between parameters, and from the correlations we can infer the importance of the different features of the global spectrum in the determination of the final bound on PEP violation. We will show in the results section that the analysis method of this work achieved compatible uncertainty in the number of events.
However we need to remark that, even though the uncertainties are compatible at the numerical level, the result from this work has taken into account contributions from systematics that could not be well evaluated using the spectra subtraction. It is important to note the improvement in the control of the systematics that is not self-evident in the numerical result. The input of the background source is the gamma radiation, with the rate and energy distribution taken from published measurement inside the tunnel of the Gran Sasso laboratory.
A realistic setup that includes the SDDs and the scintillator detectors, the copper conductor and the aluminum vacuum chamber, as shown in Fig. Three types of simulations were performed in the framework of this study. The first type is for the background originating from gamma rays inside the laboratory. As the input of the energy distribution and the rate of the gamma radiation, we took the data from the measurement of the gamma-ray flux below keV in the underground Hall A of LNGS [ 29 ].
The flux was applied uniformly to the outer surfaces of the aluminum box, and the energy deposit at the SDDs is smeared by a Gaussian distribution with eV FWHM to represent the detector resolution. By normalizing the statistics of the simulation result to 30 days of data taking, we obtained an estimated spectrum for six SDDs, which reproduces to leading order the data without DC current, as shown in Fig.
This result will be a future guide line when the passive shielding is implemented and the cosmic ray background becomes dominant for the measurement. The last type of simulation was done to determine the effective detection efficiency of the fluorescence X-rays near 8 keV for the SDDs.
For this purpose, 8 keV photons are generated at a random position inside the copper strip with random initial direction. As a result, the detection efficiency factor, which is used in the calculation of the PEP probability in the later section, was estimated to be about 1. The Monte Carlo simulation result as shown in the inset of Fig. Although the Monte Carlo model needs to be refined to account for the overestimate of the background rate, it is clearly confirmed that the environmental gamma radiation is the dominant background source.
Based on the experience of the VIP experiment that the passive shielding will reduce such background by at least a factor of 10, the background due to environmental gamma radiations with the complete shielding is expected to be less than 5 events per day in the energy region of interest. Then the cosmic ray events arriving at some ten times per day become the next dominant background source, with its contribution to the energy of interest still to be studied based on future data with well-calibrated veto detectors and refined Monte Carlo model.
Further studies into more rare background sources including those introduced by the radiative isotopes inside the setup materials will follow, after we have achieved the expected background reduction with the full shielding and have a thorough understanding of the aforementioned two dominant background sources.
From the result of the simultaneous fit, we obtained the number of PEP violating events which is compatible with zero:. Past results from PEP violation tests for electrons with a copper conductor, together with the result from this work and the anticipated goal of VIP-2 experiment. The result 1 is based on the same data set of this work, but using the spectra subtraction in the analysis.
We obtained a new upper limit of the probability that the Pauli Exclusion Principle can be violated, from the first three months of data taking in the VIP-2 experiment. As shown in Fig. We introduced for the first time into the analysis the simultaneous fit of the background spectrum and the signal spectrum. This method eliminated the uncertainties in the normalization of the spectra and the choice of the ROI, which introduce systematic errors in the spectra subtraction method that were never evaluated quantitatively in previous experiments.
With improved control of the systematic error, the upper limit determined from the new analysis is numerically compatible with our previously published result [ 12 ] marked as 1 in Fig.
The improvement compared to 1 came from more accurate Monte Carlo simulation for the detection efficiency factor. The Ramberg and Snow formula Eq. A thorough review including comparison of the different experimental methods and new interpretations of the Ramberg—Snow type measurement requires an in-depth investigation of the atomic and solid-state physics models of the interactions of free electrons in metal, and we plan to dedicate a forthcoming paper to this topic. In the next steps of the experiment, the passive shielding with circulated nitrogen gas shown schematically in Fig.
Using this shielding we expect a one-order-of-magnitude reduction in background with respect to this work, leading to a factor of 3 improvement in the upper limit.
The implementation of the modifications is planned together with the installation of the passive shielding. With the complete installation of the apparatus, the planned data taking time of 3—4 years will introduce a factor of 4—5 improvement considering the upper limit roughly scales with the inverse square-root of exposure time. Greenberg, On the surprising rigidity of the Pauli exclusion principle. B Proc. Jackiw, The unreasonable effectiveness of quantum field theory, in Conceptual Foundations of Quantum Field Theory , ed.
Cao Cambridge University Press, Cambridge, Google Scholar. Bellini et al. C 81 , Elliott et al. Messiah, O. Greenberg, Phys. Ramberg, G. Snow, Phys. B , — Ignatiev, V. Kuzmin, Yad. Okun, Comments Nucl. Greenberg, A. Rahal, A. Campa, Phys. A 38 , Curceanu et al. Article Google Scholar. Bartalucci et al. Sperandio, PhD thesis. New experimental limit on the Pauli exclusion principle violation by electrons from the VIP experiment.
Tor Vergata University, Rome Fiorini et al. A , Lechner et al. Shi et al. Pichler et al. Marton et al. Okada et al. Bazzi et al. A , 7—16 Brun, F. Rademakers, Nucl. Methods Phys. A , 81—86 Penelope—a code system for Monte Carlo simulation of electron and photon transport. Bucci et al. A 41 , — Ambrosio et al. B , 18—22 Mallow, A. Freeman, J. Desclaux, Phys. A 17 , Indelicato, Nucl. B 31 , 14—20 Download references. We thank H. Schneider, L. Stohwasser, and D. Furthermore, this paper was made possible through the support of a grant from the John Templeton Foundation ID The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation.
Fermi 40, Frascati, , Rome, Italy. Shi, S. Bartalucci, M. Bazzi, A. Bragadireanu, M. Cargnelli, A. Clozza, L. De Paolis, C. Guaraldo, M. Iliescu, J. Marton, M. Miliucci, A. Pichler, D. Pietreanu, K. Piscicchia, A. Scordo, D. Sirghi, F. Sirghi, L. Sperandio, O. Vazquez Doce, J. Shi, M. Cargnelli, J. Marton, A. Pichler, E. Bragadireanu, D. Pietreanu, D. Box You can also search for this author in PubMed Google Scholar.
Correspondence to H. This program solves the multiconfiguration Dirac—Fock equations self-consistently, taking into account relativistic effects.
Specifically, the effects of the Breit operator, the Lamb shift and radiative corrections vacuum polarization and the Uehling potential are all included in the calculation that however excludes the formation of electron-positron pairs no-pair approximation. Muons and electrons can be treated in an analogous way in the self-consistent field theory. In the first step, a functional form for the wave function is defined in terms of a linear combination of a hydrogen-like basis. The coefficients of the linear combination act as variational parameters.
Then an expression for the total energy is derived in terms of these parameters, and their values are obtained through energy minimization. Usually, a further constraint is imposed, i. However, in the present case, this condition is relaxed for one electron, that is supposed to violate the Pauli principle vPp. As a result, the exchange integrals between the vPp electron and other electronic states vanish and the vPp electron can jump to any of the atomic shells, even doubly occupied.
Notice that the latter constraint is actually valid at the atomic level, because of the spherical symmetry of the atom, and only approximately for copper in solid state see below.
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