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We present a new approach which employs a deep neural network to obtain parameters of analytical representation of potential energy curve of diatomic molecule. We test the approach to find spectroscopic characteristics for the ground X2Σ+ electronic state of MgF molecule based on the experimental energies of ro-vibrational transitions. The result shows that a deep neural network can be applied in characterisation of interatomic potential of diatomic molecule. Our approach is competitive with those obtained using other methods tested, i.e. shallow neural network and the so-called brute force method.

Previous characterization of the double-well E

Melanoma is one of the most lethal and rapidly growing cancers, causing many deaths each year. This cancer can be treated effectively if it is detected quickly. For this reason, many algorithms and systems have been developed to support automatic or semiautomatic detection of neoplastic skin lesions based on the analysis of optical images of individual moles. Recently, full-body systems have gained attention because they enable the analysis of the patient’s entire body based on a set of photos. This paper presents a prototype of such a system, focusing mainly on assessing the effectiveness of algorithms developed for the detection and segmentation of lesions. Three detection algorithms (and their fusion) were analyzed, one implementing deep learning methods and two classic approaches, using local brightness distribution and a correlation method. For fusion of algorithms, detection sensitivity = 0.95 and precision = 0.94 were obtained. Moreover, the values of the selected geometric parameters of segmented lesions were calculated and compared for all algorithms. The obtained results showed a high accuracy of the evaluated parameters (error of area estimation &lt, 10%), especially for lesions with dimensions greater than 3 mm, which are the most suspected of being neoplastic lesions.

Method of ro-vibrational cooling of Cd2 and Yb2 molecules occupying initially their excited ro-vibrational levels in the ground electronic state is proposed. The method employs the c31u(53P2)↔X10g+...

Spectroscopic rotational characterization of two υ ′ = 0 and υ ′ = 1 vibrational components of the E 3 Σ 1 + ( 5 s 6 s 3S1) Rydberg state of CdNe van der Waals (vdW) complex has been performed using specially designed approach. In optical–optical double resonance (OODR) process, a selective J-excitation has been realized using the E 3 Σ 1 + ← A 3 Π 0 + ( 5 s 5 p 3P1) transition, with υ ″ = 0 level of the A 3 Π 0 + state as an intermediate in the excitation from υ = 0 of the X 1 Σ 0 + ( 5 s 2 1S0) state. As a result, B υ = 0 ′ and B υ = 1 ′ rotational constants have been determined as well as the R e ′ equilibrium internuclear separation in the E 3 Σ 1 + - state potential well.

A method of experimental selection of molecular isotopologues using optical-optical double resonance (OODR) scheme and supersonic beam source of van der Waals (vdW) complexes is presented. Due to an appropriately large isotopic shift, the proper choice of a wavenumber of a sufficiently narrowband laser in the first transition of OODR scheme can lead to a selective isotopologue excitation to the intermediate state. Thanks to this approach, it is possible to select some of the isotopologues which subsequently give a contribution to laser induced fluorescence (LIF) signal originated from the final state of OODR. In this article, results of tests of the proposed method that employs the E 3 Σ 1 + ← A 3 Π 0 + ← X 1 Σ 0 + transitions in two vdW complexes, CdKr and CdAr, are presented and analysed.

Revisited study of the E3Σ1+ (63S1) ← A3Π0+(53P1) transition in CdAr using both theoretical and experimental approach is presented. Systematic detection of the E3Σ1+ in,υ' ← A3Π0+,υ″ = 6 transition frequencies with higher accuracy and spectrally narrower laser extended and improved analysis and simulation of the LIF excitation spectrum. More consistent characterization of the E3Σ1+in-Rydberg state inner well using inversed perturbation approach methodology was achieved. Free ← bound transitions in the E3Σ1+ in ← A3Π0+,υ″ = 6 excitation were taken into account in the analysis and simulation of the recorded spectrum. The updated spectroscopic characterization of the A3Π0+ state was also revisited.

Schemes for internal ro-vibrational cooling in Yb2 and Cd2, as well as 171Yb Bohm's spin-1/2 particle version of the Einstein‒Podolsky‒Rosen experiment based on photo-dissociation of (171Yb)2 are p...

A critical review of experimental studies and ab initio calculations of the low-lying ungerade excited and ground state interatomic potentials of Cd2 van der Waals dimer is presented. Consistency as well as discrepancies between experimental results and ab initio calculations are probed. In order to obtain better agreement with existing experimental data, fill in gaps in current knowledge and provide a unifying framework, advanced all-electron ab initio calculations were performed and simulations of the reported spectra were executed. From simulations of laser-induced fluorescence excitation and dispersed emission spectra, analytical and/or point-wise representations of the (51P1), B11u(51P1), a31u(53P1), (53P1) and c31u(53P2) excited-, and the (51S0) ground-state Cd2 interatomic potentials were obtained. The comparison of the ab initio calculated potentials with results of the analyses allows to illustrate a current state-of-the-art of theory-and-experiment correspondence for such a demanding sys...

Often, experimental spectra with only partially resolved rotational structure are observed. In such cases, determination of potential energy curves for the corresponding electronic states might be not as reliable as in the high resolution studies. In this paper, we estimate the uncertainties of the potential energy curve parameters, obtained from spectra with partially or not resolved rotational structure, where both frequencies and intensities are fitted. As an example, recently reported excitation spectrum of the B 3 1(5 3 P 1 ) ← X 1 0 + (5 1 S 0 ) electronic transition in CdAr van der Waals complex is used. Two types of Morse functions are used to model the excited state potential, but method can be readily extended to more complex potential functions. It is shown, that for reliable estimation of the uncertainties of given potential function one should take into account the possible variation of the transition dipole moment function.

A theoretical study of the relatively unexplored area of low-lying Rydberg states of van der Waals molecules (vdW) in the particular case of the CdAr system is presented. The fully ab initio calculation of the potential energy curves (PECs) of the excited vdW complex CdAr above the $(5s6s)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}3}S_{1},^{\phantom{\rule{0.16em}{0ex}}1}S_{0}$ atomic asymptotes, reaching the $(5s6p)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}3}P_{0,1,2}, (5s5d)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}1}D_{2}{,}^{3}{D}_{1,2,3}, (5s6p)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}1}P_{1}$, and $(5s7s)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}3}S_{1},^{\phantom{\rule{0.16em}{0ex}}1}S_{0}$, is performed. All the calculated PECs of the Rydberg states of $\mathrm{\ensuremath{\Sigma}}$ symmetry exhibit undulations resulting in the double-well character that was already observed experimentally in the case of the lowest Rydberg states of various 12 group metal--rare gas vdW complexes. The outer wells obtained within the present work are shallow with depths not exceeding 20 ${\mathrm{cm}}^{\ensuremath{-}1}$ below the atomic asymptote and reaching equilibrium distance of roughly 27 bohr in the case of states correlating with the $(5s7s)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}3}S_{1},^{\phantom{\rule{0.16em}{0ex}}1}S_{0}$ asymptotes. The largest calculated values of permanent electric dipoles at equilibrium distances exceed 10 D in the case of ${}^{1}\mathrm{\ensuremath{\Sigma}}$ Rydberg states correlating with $(5s6p)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}1}P_{1}$ and $(5s5d)\phantom{\rule{0.16em}{0ex}}^{\phantom{\rule{0.16em}{0ex}}1}D_{2}$ atomic asymptotes. The calculations were performed within the second-order multireference perturbation theory. The performance of this particular theoretical ab initio approach is discussed in the context of the considered type of systems and compared, wherever it was possible, with the benchmark results of the coupled-cluster method obtained in this work, with other ab initio calculations based on multireference perturbation theory and experimental data.

Expansion of Zn2 or ZnRg (Rg = rare gas atom) in a molecular supersonic beam constitutes a considerable technical challenge due to the high zinc melting point and high zinc reactivity with stainless steel at high temperatures. In order to overcome these difficulties and meet the requirements for spectroscopy of van der Waals molecules containing zinc, a high-temperature source-module of the supersonic molecular beam for aggressive elements was designed. The module was tested in the laser-induced fluorescence excitation spectroscopy experiment using the b30u+43P1←X10g+(41S0) bound ← bound transitions in Zn2. The new source-module can be used for other aggressive elements for which a laser-vaporization technique has been used to date.

Multichannel dispersed emission spectra originated upon a selective excitation of Rydberg electronic energy states in the ZnAr and CdAr van der Waals (vdW) complexes are simulated and analysed as a proof-of-concept of the future experimental approach. Simulations of the emission spectra are based on ab-initio calculated interatomic potentials and transition dipole moments (TDMs), that for ZnAr were newly calculated. Experimental set-up that is under construction along with the experimental procedure are discussed.

Revisited study of the E

A new method for obtaining a pointwise potential energy curve of diatomic molecule using Neural Network is reported. The method is employed to generate new characteristics of the B11u(51P1) electronic state of Cd2 based on LIF excitation spectrum previously recorded using the B11u←X10g+ (51S0) transition. The obtained potential provides better simulation-to-experiment agreement than those obtained using other methods. Correctness of the method is additionally tested on artificially generated LIF excitation spectra based on well characterized b30u+(53P1)←X10g+ transition in Cd2. A method for obtaining parameters of an analytical form of the potential using Neural Network applied on artificially generated Cd2 spectra is also presented.

Profiles of the (υ′;υ″ = 0) vibrational bands recorded using the b30+u ← X10g+ and B31 ← X10+ transitions in Cd2 and CdAr complexes, respectively, are presented and analysed. Specifically, CdAr and Cd2 complexes are simultaneously propagating in a supersonic beam. Transitions in these complexes can be used to provide the conditions for selective detection of one of the complexes in the expansion. Extended analysis of the B31- and b30+u -state vibrational progressions provided improved values for ω′ex′e and ω′e vibrational characteristics, as well as D′e well depths and Re′ bond lengths of the B31- and b30+u-state potentials. Several of the CdAr bands were recorded with partly resolved rotational structure. The new characterisation of the B31 state, along with results of the rotational and isotopic analyses of the band profiles, agrees with the most recent results of ab initio calculations, while results obtained for the b30+u state call for improvement in the ab initio calculations for Cd2.

Excitation spectra of CdNe, CdAr and CdKr complexes were recorded using the B31(53P1) ← X10+(51S0) bound ← bound and free ← bound transitions. A simulation of the dissociation continua formed by the free ← bound transitions in CdNe and CdAr permitted a determination of the repulsive part of the B31-state potential above the dissociation limit. The bound ← bound transitions in the excitation spectra of CdNe, CdAr and CdKr, and those previously recorded for CdHe and CdXe, were analyzed; by including their rotational structure and isotopic composition in the analysis, the characterization was improved. Morse functions for CdNg (Ng = noble gas) (also Lennard-Jones (12-6) for CdHe) and ab initio calculated interatomic potentials were tested for the representation of the B31-state potential above and below the dissociation limit. It was also found that previously reported ab initio calculated potentials for CdNe, CdAr, CdKr and CdXe could be modified and used. The B31-state rotational constants could be determined from the simulation of the ( υ ′ ; υ ″ ) = (2; 0)-band rotational profile in CdAr.

Analysis of profiles of ( υ ′; υ ″ = 0) vibrational bands, ( υ ′ = 0,1,2,4,5), recorded with partly resolved rotational structure using the B 3 1(5 3 P 1 ) ← X 1 0 + (5 1 S 0 ) transition in CdAr is presented. The analysis allowed for determination of the B v ′ and D v ′ rotational constants, and new values of ω e ′ vibrational frequency and D e ′ well depth of the B 3 1-state interatomic potential. The new characterization of the B 3 1 state in CdAr is closer to the result of recent ab initio calculations [Chem. Phys. Lett. 471 (2009) 29] than results of our previous study performed with vibrational resolution [Spectrochim. Acta A 56 (2000) 1613].

Comprehensive spectroscopic study of CdKr van der Waals complex in its Rydberg electronic energy state E 3 Σ 1 + ( 5 s 6 s 3 S 1 ) , using OODR process from the ground X 1 Σ 0 + ( 5 s 2 1 S 0 ) state via the intermediate A 3 0 + ( 5 s 5 p 3 P 1 ) or B 3 1 ( 5 s 5 p 3 P 1 ) states, is presented. Detection of the E 3 Σ 1 + , υ ′ ← A 3 0 + , υ ″ and E 3 Σ 1 + , υ ′ ← B 3 1 , υ ″ transition frequencies with higher accuracy and spectrally narrower laser extends previous analyses and simulations of laser induced fluorescence (LIF) excitation spectra. Potential energy curve of the E 3 Σ 1 + state exhibits double-well structure with inner (deeper) E 3 Σ 1 in + and outer (shallower) E 3 Σ 1 out + wells. More reliable characterization of both wells using inversed perturbation approach (IPA) methodology is achieved.

The method of supersonic free-jet expansion beam combined with techniques of laser spectroscopy was used in an investigation of vibronic and isotopic structures in the D 1 0 u + (6 1 S 0 ) and F 3 1 u (6 3 P 2 ) electronic energy Rydberg states of Cd 2 . Laser-induced fluorescence excitation spectra recorded using the D 1 0 u + ← X 1 0 g + (5 1 S 0 ) and F 3 1 u ← X 1 0 g + transitions in the region of 206-218 nm provided spectroscopic characteristics of the excited states and allowed constructing of their intratomic potentials. Isotopic structures recorded in the (v',v") bands of the D 1 0 u + ← X 1 0 g + transition were used in determination of the D 1 0 u + state vibrational characteristics (ω' e x' e , ω' e x' e ) and v' assignment The v 0,0 recorded directly in the F 3 1 u ← X 1 0 g + transition enabled determination of the bottom of the F 3 1 u state potential well. Valence ab initio calculations of Cd 2 interatomic potentials were performed with relativistic and spin-orbit effects taken into account. The experimental results were compared with results of the ab initio calculations. A free-jet expansion of Cd 2 as a source of entangled atoms for a test of Bell's inequality was analyzed.

Isotopic and rotational structures of the ( υ ′, υ ″) = (13,5), (14,5), (16,5) and ( υ ′, υ ″) = (0,1)–(6,1) vibrational bands of the E 3 Σ + ← A 3 Π 0 + and E 3 Σ + ← B 3 Σ 1 + transitions in CdAr, respectively, as well as the ( υ ′, υ ″) = (21,9) of the E 3 Σ + ← A 3 Π 0 + transition in CdKr were investigated using free-jet expansion beam and laser excitation. An optical–optical double resonance process was employed from the X 1 Σ 0 + + to the E 3 Σ + Rydberg via the A 3 Π 0 + or B 3 Σ 1 + intermediate electronic state. The structure of the bands with resolved isotopic structure was analyzed including their rotational structure. Analysis and simulation of the bands provided values for vibrational and rotational characteristics of the states. The analysis extended our previous low-resolution studies performed for the E 3 Σ + ← A 3 Π 0 + and E 3 Σ + ← B 3 Σ 1 + transitions.

New ab initio and revisited experimental studies of the interatomic potentials of ungerade excited and ground electronic energy states of the heavy van der Waals (vdW) dimer Hg2 were used as a “test-bed” for theory-to-experiment comparisons. Representations of the lowest excited- and ground-state Hg2 interatomic potentials were proposed, by using a new analytical approach as well as by using an inverted perturbation approach (IPA). The comparison of the new ab-initio calculated potentials with the results of the analyses illustrates an improved theory-to-experiment agreement for demanding heavy systems such as Hg2.

A new determination of the equilibrium distance Re′ out of the E3Σ+(63S1)-state potential outer well in CdAr is reported. The value was obtained taking into consideration both previously measured [Urbanczyk et al., Chem. Phys. Lett. 503 (2011) 18] excitation spectrum of the E3Σ+ ← B3Σ1+ (53P1) transition originated from υ″ = 1 as well as newly observed spectrum originating from υ″ = 2. In this study we also confirm values of ωe′ and ωe′χe′ vibrational constants of E3Σ+-state outer well.

Results of new all-electron ab initio calculations and revisit of experimental studies of the interatomic potentials of lower-lying ungerade excited and ground electronic energy states of the Hg_{2} and Cd_{2} van der Waals complexes are used as probes of discrepancies between theory and experiment. From simulations of the previously and presently measured LIF excitation and dispersed emission spectra new analytical representations of the excited- and the ground-state interatomic potentials are proposed. An inverted perturbation approach was also used to improve the studied interatomic potentials. The comparison of the new ab-initio calculated potentials with the results of the analyses illustrates an improve theory-to-experiment agreement for such a demanding system like Hg_{2} or Cd_{2}.

Application of a modified version of high-temperature high-pressure all-metal pulsed source of supersonic molecular beam is demonstrated in a production of van der Waals (vdW) complexes. The vdW complexes are produced possessing controllable rotational temperature (T rot ) in the range from 3 K to 19 K. An effective control over T rot is illustrated employing excitation spectrum recorded using the B 31(53 P 1) ← X 10+(51 S 0) transition in CdAr. First-time resolved rotational structure in the profile of the υ′ = 2←υ′′ = 0 vibrational component is reported. The control over T rot is crucial in a dissociation of the (111Cd)2 isotopologue in the supersonic beam. For the process, excitation at well defined J′← J′′ rotational transition within the (υ′,υ′′) = (40,0) vibrational band of the A 10 u +(51 P 1) ← X 10 g +(51 S 0) transition is employed. It is followed by the dissociation using A 10 u +(υ′ = 40,J′′) → X 10 g + bound → free transition. An analysis and simulation of the (40,0) vibrational band rotational structure are presented. Parameters describing conditions in the supersonic beam, degree of rotational cooling, Doppler broadening and spectral bandwidth of the laser beam are used.

An all-metal pulsed source of van der Waals (vdW) dimers was constructed; it operates at temperatures up to 1000 K and carrier gas stagnation pressures up to 10 bars. Performance of the source was demonstrated in the production and spectroscopy of both CdAr and Cd(2) molecules in a supersonic beam expansion. Simulation of the recorded laser induced fluorescence (LIF) excitation spectra using the B(3)1(5(3)P(1)) ← X(1)0(+)(5(1)S(0)) and b(3)0(u)(+)(5(3)P(1))←X(1)0(g)(+)(5(1)S(0)) transitions in CdAr and Cd(2), respectively, showed that these molecules were produced with a rotational temperature in the range from 3 K to 19 K. The source was incorporated into an experimental set-up dedicated to the realization of Bohm's spin-1/2 particle version of the Einstein-Podolsky-Rosen experiment for ((111)Cd)(2) molecules.

The method of supersonic free-jet expansion beam combined with techniques of laser spectroscopy was used in an investigation of vibronic and isotopic structures in the D¹0(u)⁺ (6¹S₀) and F³1(u)(6³P₂) electronic energy Rydberg states of Cd₂. Laser-induced fluorescence excitation spectra recorded using the D¹0(u)⁺ ← X¹0(g)⁺(5¹S₀) and F³1(u) ← X¹0(g)⁺ transitions in the region of 206-218 nm provided spectroscopic characteristics of the excited states and allowed constructing of their intratomic potentials. Isotopic structures recorded in the (υ',υ'') bands of the D¹0(u)⁺ ← X¹0(g)⁺ transition were used in determination of the D¹0(u)⁺ state vibrational characteristics (ω'(e)x'(e), ω'(e)x'(e)) and υ' assignment. The ν(0,0) recorded directly in the F³1(u) ← X¹0(g)⁺ transition enabled determination of the bottom of the F³1(u) state potential well. Valence ab initio calculations of Cd₂ interatomic potentials were performed with relativistic and spin-orbit effects taken into account. The experimental results were compared with results of the ab initio calculations. A free-jet expansion of Cd₂ as a source of entangled atoms for a test of Bell's inequality was analyzed.