# Colliding and Fixed Target Mode in a Single Experiment—A Novel Approach to Study the Matter under New Extreme Conditions

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## Abstract

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## 1. Introduction

## 2. The Triple Nuclear Collisions Method

#### 2.1. Rate Estimates of the Triple Nuclear Collisions

#### 2.2. Discussion of Different Types of Fixed Targets

**Option SFT1.**A super-thin SFT made of the graphene layer of thickness ${l}_{g}\ll 3.32\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$m. In this case, the TNC rate of Equation (1) has to be multiplied by the factor $100\xb7\frac{{l}_{g}}{2R}\frac{1.43}{2.2}$, and we obtain ${\frac{d{N}_{p+C+p}}{dt}}_{graphene}\simeq \frac{{l}_{g}}{2R}\xb7{10}^{-5}\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}$ for the p+C+p collisions. We have taken into account the different target thicknesses and the fact that graphene has a density of $1.43$ g·cm${}^{-3}$, which is essentially lower than carbon. Evidently, a too thin target may significantly reduce the rate of the TNC. Apparently, such a target can be used just for testing the new technology for TNC measurements, since the resulting reaction rate is still low.

**Option SFT2.**A rotating and restorable SFT. In our estimates of the reaction rate of Equation (1) for the traditional assembling of the target, we assumed the geometrical thickness of the target to be ${l}_{g}=3.32\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$m. However, our analysis of the energy deposition to the target shows that the geometrical thickness target ${l}_{g}$ can be increased by a factor of 30 or even 100, i.e., one can employ ${l}_{g}\in 100\u2013332\phantom{\rule{0.166667em}{0ex}}\mathsf{\mu}$m if it rotates with the linear speed of 30–100 m/s. In this case, one can expect an additional increase in the reaction rate by a factor of 30–100, which, in total, gives us a sizable enhancement of the reaction rate (1) by 3000–10,000 times. The latter estimate seems to be feasible for the TNC detection, not only for the p+C+p reactions, but also for the Pb+Pb+Pb ones. However, for the TNC experiments with heavy nuclei, it is perhaps more realistic to consider a stronger target made of bismuth (Bi) or tungsten (W).

**Option SFT3.**A jet micro-powder (pellet) target successfully operated at the electron storage ring [37] with its target thickness for the Ni micro-powder particles, with a diameter of approximately 1 $\mathsf{\mu}$m being approximately ${\tau}_{Ni}\simeq {10}^{16}$ atoms·cm${}^{-2}$ [38]. Taking into account recent technological advances, one can hope that such targets will be revisited with a significantly increased density of jet micro-powder for the Pb, Wi or W particles. Moreover, it might be possible for the modern jet micro-powder targets to provide a sufficiently higher speed of particle flow to essentially reduce the energy deposition effects discussed above.

**Option 4.**The cardinal solution to this problem could be a construction of a (vertically oriented) storage ring with a high-intensity ion beam that is focused toward the interaction region of two collider beams with a submicron size and a similar positioning accuracy. Even the expected density of an ion beam of ${10}^{21}$ ions/cm${}^{3}$ can be used for the TNC experiments in the nearest future, while one can hope that, in a few years, this density of ions in the beam can be increased further.

## 3. Possible Signatures of TNC

## 4. Evolution of Matter in Central Cell in Pb+Pb+Pb Collisions

## 5. Conclusions and Perspectives

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Schematic picture of the interaction (intersection) volume of two identical beams A and B of a radius R. The angle between beams is $\alpha =5\xb7{10}^{-4}$ rad [53] and $\left|BC\right|\simeq 2R$. The bar interior of this volume shows a traditional arrangement of target, as discussed below.

**Figure A2.**Scheme of the interaction process of two colliding nuclei A and B with the nucleus of the target T with the geometrical radii ${R}_{A}$, ${R}_{B}$ and ${R}_{T}$, respectively. The interaction volume ${V}_{T\in A+B}^{int}$ is defined by the distance between the surfaces of nuclei A and B, which is $2{R}_{T}+{t}_{del}$, and by the maximal geometrical size of nuclei A and T. For such a configuration of nuclei, the TNC will occur with a probability equal to 1. The mean value for ${V}_{T\in A+B}^{int}$ is provided by averaging over the distance ${\lambda}_{A}$ between the surfaces of a nucleus A and the target T. Similar averaging over the nucleus B position should be performed as well.

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**Figure 1.**Schematic picture of the p+C+p TNC at the center-of-mass collision energy of protons $\sqrt{s}=2.76$ TeV. It visualizes the results of the UrQMD 3.4 simulations for $t=5$ fm (

**left panel**) and for $t=8.4$ fm (

**right panel**) after first collision of protons. The volume ${V}_{h}$ of particles is proportional to their mass ${m}_{h}$ for a better perception. The encircled nucleon shown in both panels does not leave its position during the reaction.

**Figure 2.**Schematic picture of the non-central Pb+Pb+Pb TNC with time delay ${t}_{del}=10$ fm at the center-of-mass collision energy of beam ions $\sqrt{s}=2.76$ TeV. It visualizes the results of the UrQMD 3.4 simulations: the beginning of collision of target nucleus with the right ion (

**left panel**) and the moment when the right ion almost passed through the target nucleus (

**right panel**). The volume ${V}_{h}$ of particles is proportional to their mass ${m}_{h}$ for a better perception.

**Figure 3.**Comparison of the pseudorapidity distributions of charged particles $\frac{d{N}_{ch}}{d\eta}$ found in the experiments with the ones obtained by the UrQMD simulations. (

**Left panel**): ALICE data on inelastic p+p collisions of Ref. [40] measured at minimum bias at $\sqrt{{s}_{NN}}=2.76$ TeV (symbols) vs. the UrQMD results (solid curve). For comparison, the dashed curve shows the same distribution for the p+C+p TNC. (

**Right panel**): ALICE data of Ref. [16] measured in 0–5% most central Pb+Pb collisions at $\sqrt{{s}_{NN}}=2.76$ TeV (symbols) vs. the UrQMD results (solid curve). The dashed curve shows the same distribution for the Pb+Pb+Pb TNC.

**Figure 4.**Comparison of the ${p}_{T}$ spectra of kaons found in the experiments with the ones obtained by the UrQMD simulations. The solid curve shows the results of BC, whereas the dashed curve shows the results for TNC. (

**Left panel:**) ALICE data on inelastic p+p collisions of Refs. [41,42,43] measured at minimum bias (symbols) vs. the UrQMD results for the p+p BC and for the p+C+p TNC. (

**Right panel:**) ALICE data of Ref. [16] measured in 0–5% most central Pb+Pb collisions vs. the UrQMD results for the Pb+Pb BC and for the Pb+Pb+Pb TNC.

**Figure 5.**Ratio of transversal momentum spectra of TNC to the one of A+A collisions (3-to-2 nuclei modification factor) of hadrons obtained for the same collision energy $\sqrt{{s}_{NN}}=2.76$ TeV as a function of particle transverse momentum with the ones obtained by the UrQMD simulations. (

**Left panel:**) Results for the p+C+p TNC are found at $\left|y\right|<0.5$. (

**Right panel:**) Results for the Pb+Pb+Pb TNC are found at $\left|y\right|<0.1$.

**Figure 6.**Comparison of the hadronic yields found for the central Pb+Pb BC (filled symbols) and for the central-simultaneous Pb+Pb+Pb TNC (open symbols) as the function of particle rapidity y.

**Figure 7.**The time evolution of the central cell baryonic charge density of the volume 27 fm${}^{3}$ during the process of ordinary BC collisions (filled symbols) and the TNC (empty symbols) for $\sqrt{{s}_{NN}}=200$ GeV (triangles pointing upwards) and for $\sqrt{{s}_{NN}}=2.76$ TeV (triangles pointing downwards). The time ${t}_{0}$ is the moment at which the remnants of projectile nuclei have passed through the central cell.

**Figure 8.**The evolution of central cell parameters in the $T\u2013{\mu}_{B}$ plane obtained with the MIT bag model equation of state [45]. The filled symbols correspond to the Pb+Pb collisions, whereas the empty ones correspond to the Pb+Pb+Pb TNC. Collision energy $\sqrt{{s}_{NN}}=200$ GeV points are shown by the triangles pointing upwards, whereas the evolution trajectories for the energy $\sqrt{{s}_{NN}}=2.76$ TeV are shown by the triangles pointing downwards. The topmost points correspond to the time $t-{t}_{0}>1$ fm. The curve of pseudo-critical temperature corresponds to a lattice QCD parameterization [48], whereas the crosses correspond to the parameters of chemical freeze-out in Pb+Pb collisions found in Refs. [49,50,51]. The collision energies of given chemical freeze-out points of Pb+Pb collisions are as follows (from left to right): $\sqrt{{s}_{NN}}=2760,200,130,62.4,17.3,12.3$ GeV [49,50,51].

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**MDPI and ACS Style**

Vitiuk, O.V.; Pugatch, V.M.; Bugaev, K.A.; Yakovenko, N.S.; Panasiuk, P.P.; Zherebtsova, E.S.; Dobishuk, V.M.; Chernyshenko, S.B.; Grinyuk, B.E.; Sagun, V.;
et al. Colliding and Fixed Target Mode in a Single Experiment—A Novel Approach to Study the Matter under New Extreme Conditions. *Particles* **2022**, *5*, 245-264.
https://doi.org/10.3390/particles5030022

**AMA Style**

Vitiuk OV, Pugatch VM, Bugaev KA, Yakovenko NS, Panasiuk PP, Zherebtsova ES, Dobishuk VM, Chernyshenko SB, Grinyuk BE, Sagun V,
et al. Colliding and Fixed Target Mode in a Single Experiment—A Novel Approach to Study the Matter under New Extreme Conditions. *Particles*. 2022; 5(3):245-264.
https://doi.org/10.3390/particles5030022

**Chicago/Turabian Style**

Vitiuk, Oleksandr V., Valery M. Pugatch, Kyrill A. Bugaev, Nazar S. Yakovenko, Pavlo P. Panasiuk, Elizaveta S. Zherebtsova, Vasyl M. Dobishuk, Sergiy B. Chernyshenko, Borys E. Grinyuk, Violetta Sagun,
and et al. 2022. "Colliding and Fixed Target Mode in a Single Experiment—A Novel Approach to Study the Matter under New Extreme Conditions" *Particles* 5, no. 3: 245-264.
https://doi.org/10.3390/particles5030022