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arXiv:2608.07205

Atomic correlation effects in collapse-induced spontaneous radiation

Simone Manti, Nicola Bortolotti, Lajos Diósi, Kristian Piscicchia, Catalina Curceanu

quant-phSubmitted Aug 7, 2026• Announced Aug 10, 2026• 0 citations

Abstract

Collapse models introduce stochastic and nonlinear modifications in the quantum dynamics, predicting observable effects, such as spontaneous radiation from charged particles, which can be used to constrain their parameters. Recently, attention has focused on the 1-100 keV energy range, where the wavelength of the emitted photons becomes comparable to atomic dimensions, making the emission sensitive to atomic structure and leading to model-dependent behaviors that enable their discrimination. Here, we derive a general expression for the spontaneous emission rate for arbitrary noise, providing a framework that systematically incorporates the atomic structure through the radial distribution of the emitters, modulated by the specific collapse model. The formalism recovers previous results in the appropriate limits and naturally includes new low-energy effects, such as cancellation mechanisms arising from charge correlations. We evaluate the rates for germanium and xenon within the Diósi-Penrose and Continuous Spontaneous Localization models, showing how these correlations modify the predicted emission rates. This approach provides a unified framework to account for atomic effects and enables more robust, material-dependent experimental constraints on collapse model parameters.

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Collapse models introduce stochastic and nonlinear modifications in the quantum dynamics, predicting observable effects, such as spontaneous radiation from charged particles, which can be used to constrain their parameters. Recently, attention has focused on the 1-100 keV energy range, where the wavelength of the emitted photons becomes comparable to atomic dimensions, making the emission sensitive to atomic structure and leading to model-dependent behaviors that enable their discrimination. Here, we derive a general expression for the spontaneous emission rate for arbitrary noise, providing a framework that systematically incorporates the atomic structure through the radial distribution of the emitters, modulated by the specific collapse model. The formalism recovers previous results in the appropriate limits and naturally includes new low-energy effects, such as cancellation mechanisms arising from charge correlations. We evaluate the rates for germanium and xenon within the Diósi-Penrose and Continuous Spontaneous Localization models, showing how these correlations modify the predicted emission rates. This approach provides a unified framework to account for atomic effects and enables more robust, material-dependent experimental constraints on collapse model parameters.

Abstract We study spontaneous radiation emission from matter, as predicted by the Continuous Spontaneous Localization (CSL) collapse model. We show that, in an appropriate range of energies of the emitted radiation, the largest contribution comes from the atomic nuclei. Specifically, we show that in the energy range

E\sim 10\,-\,10^{5}

E ∼ 10 - 10 5 keV the contribution to the radiation emission from the atomic nuclei grows quadratically with the atomic number of the atom, overtaking the contribution from the electrons, which grows only linearly. This theoretical prediction is then compared with the data from a dedicated experiment performed at the extremely low background environment of the Gran Sasso underground National Laboratory, where the radiation emitted form a sample of Germanium was measured.As a result, we obtain the strongest bounds on the CSL parameters for

r_C\le 10^{-6}

r C ≤ 10 - 6 m, improving the previous ones by more than an order of magnitude.

We report on the search for x-ray radiation as predicted from dynamical quantum collapse with low-energy electronic recoil data in the energy range of 1-140 keV from the first science run of the XENONnT dark matter detector. Spontaneous radiation is an unavoidable effect of dynamical collapse models, which were introduced as a possible solution to the long-standing measurement problem in quantum mechanics. The analysis utilizes a model that for the first time accounts for cancellation effects in the emitted spectrum, which arise in the x-ray range due to the opposing electron-proton charges in xenon atoms. New world-leading limits on the free parameters of the Markovian continuous spontaneous localization and Diósi-Penrose models are set, improving previous best constraints by two orders of magnitude and a factor of five, respectively. For the strength and correlation length of the continuous spontaneous localization model, values in the originally proposed parameter ranges are experimentally excluded for the first time.

We report on the search for x-ray radiation as predicted from dynamical quantum collapse with low-energy electronic recoil data in the energy range of 1–140 keV from the first science run of the XENONnT dark matter detector. Spontaneous radiation is an unavoidable effect of dynamical collapse models, which were introduced as a possible solution to the long-standing measurement problem in quantum mechanics. The analysis utilizes a model that for the first time accounts for cancellation effects in the emitted spectrum, which arise in the x-ray range due to the opposing electron-proton charges in xenon atoms. New world-leading limits on the free parameters of the Markovian continuous spontaneous localization and Diósi-Penrose models are set, improving previous best constraints by two orders of magnitude and a factor of five, respectively. For the strength and correlation length of the continuous spontaneous localization model, values in the originally proposed parameter ranges are experimentally excluded for the first time.

One way to solve the long-standing ``measurement''problem in quantum mechanics is to modify Schr\"odinger's equation so that the collapse of a state vector is the result of some intrinsic physical dynamics. The introduction of such collapse dynamics often results in energy nonconservation. In this paper, we first derive a general expression for the rate of change in the expectation value of energy in a general collapse model that supports a linear evolution of the density matrix. In particular, we show, under certain plausible assumptions, that energy nonconservation is an inevitable consequence of collapse. We then work with a specific model, namely, the nonrelativistic continuous spontaneous localization (CSL) model, to derive further consequences of collapse. In CSL, in a nonunitary evolution, a particle interacts with a fluctuating scalar field, leading to the collapse of the state vector. One consequence of this interaction is that a free electron can radiate spontaneously. We calculate the spectrum of this radiation. The result is then compared with the observed upper bound on spontaneous radiation in Ge and a constraint on the parameters of CSL is obtained.

The work presented in this paper aimed to obtain new, more stringent, limits on the parameters of the Continuous Spontaneous Localization collapse model. The result is accomplished by performing a Bayesian analysis of the X-ray emission data collected by the IGEX collaboration, compared with the spontaneous photon emission which is predicted by collapse models. The most stringent limits on the collapse rate

\lambda

and the correlation length

r_C

of the CSL model are obtained , with respect to any other method, over a broad range of the parameters space.

Collapse models consist in dynamical reformulations of the standard quantum mechanics aiming to solve the measurement problem. The standard Schrödinger dynamics is modified with the introduction of nonlinear and stochastic terms, which induce the wave function collapse in space. Collapse models predict slight deviations from the standard quantum mechanics predictions, in particular the emission of a “spontaneous radiation”, which we explored to set the most stringent limits on the collapse models parameters in a broad range. To this end, the X-ray emission data collected by the IGEX collaboration are analyzed and compared with the spectrum of the spontaneous photon emission process predicted by the theories. The results of the data analyses, and the ongoing experimental efforts will be presented.