Isotropic Emission Research Articles

Customized calibration sources in the JUNO experiment

We customized a laser calibration system and four radioactive γ-ray calibration sources for the Jiangmen Underground Neutrino Observatory (JUNO), a 20-kton liquid scintillator-based neutrino detector. The laser source system was updated to realize the isotropic light emission timing within ±0.25 nsec level and to allow the tuning of the laser intensity covering more than four orders of magnitude. In addition, methods to prepare four different radioactive sources (18F, 40K, 226Ra, and 241Am), covering energies from 0 (10) keV to 0 (1) MeV, for the JUNO detector were established in this study. The radioactivity of each source and the risk of radioactive substance leaking into the detector from the source were confirmed to meet the experimental requirements.

Radiation hydrodynamical simulations of super-Eddington mass transfer and black hole growth in close binaries

ABSTRACT Radiation-driven outflows play a crucial role in extracting mass and angular momentum from binary systems undergoing rapid mass transfer at super-Eddington rates. To study the mass transfer process from a massive donor star to a stellar-mass black hole (BH), we perform multidimensional radiation-hydrodynamical simulations that follow accretion flows from the first Lagrange point down to about a hundred times the Schwarzschild radius of the accreting BH. Our simulations reveal that rapid mass transfer occurring at over a thousand times the Eddington rate leads to significant mass-loss from the accretion disc via radiation-driven outflows. Consequently, the inflow rates at the innermost radius are regulated by two orders of magnitude smaller than the transfer rates. We find that convective motions within the accretion disc drive outward energy and momentum transport, enhancing the radiation pressure in the outskirts of the disc and ultimately generating large-scale outflows with sufficient energy to leave the binary. Furthermore, we observe strong anisotropy in the outflows, which occur preferentially toward both the closest and furthest points from the donor star. However, when averaged over all directions, the specific angular momentum of the outflows is nearly comparable to the value predicted in the isotropic emission case. Based on our simulation results, we propose a formula that quantifies the mass growth rates on BHs and the mass-loss rates from binaries due to radiation-driven outflows. This formula provides important implications for the binary evolution and the formation of merging binary BHs.

Self‐Assembled Colloidal Photonic Structures for Directional Radioluminescence of Gd and Ta Oxide Scintillators

AbstractRadiation detection is being revolutionized by integrating photonic elements into scintillators. In this study, a scalable and cost‐effective method is proposed to achieve tuneable emission enhancement across the visible spectrum by colloidal self‐assembly of photonic crystals on scintillator surfaces. This concept is demonstrated for Eu3+/Tb3+‐doped Gd and Ta oxides. Widely available and affordable colloidal nanospheres of SiO2 or polymethyl methacrylate are self‐assembled on these scintillators. The size of the nanospheres is carefully optimized to match the desired emission lines of Eu3+/Tb3+. The result is homogeneous and closely‐packed structures with clear photonic bandgap in the visible range. Under X‐ray excitation, the scintillators covered with the photonic layers exhibit enhanced light extraction in the direction perpendicular to the surface, compared to isotropic emission in the bare scintillator. Such scintillation directionality, when optically matched with a proper detector, will result in higher efficiency of the overall detection system. Moreover, X‐ray imaging demonstrates an enhancement of 25% in system resolution of the scintillator supplemented with the photonic layer compared to unmodified scintillators. The proposed method is scintillator‐ and nanosphere‐agnostic, thus offering a promising versatile approach for directing the scintillation light toward a photodetector and increasing detection system performance, including high‐resolution imaging applications.

AT2021lwx: Another Neutrino-coincident Tidal Disruption Event with a Strong Dust Echo?

We discuss the possible association of an astrophysical neutrino (IC220405B) with the recently reported, extremely energetic tidal disruption event (TDE) candidate AT2021lwx (ZTF20abrbeie, aka “Scary Barbie”) at redshift z = 0.995. Although the TDE is about 2.°6 off the direction of the reconstructed neutrino event (outside the 90% confidence level localization region), the TDE candidate shares some important characteristics with so-far-reported neutrino–TDE associations: a strong infrared dust echo, high bolometric luminosity, a neutrino time delay with respect to the peak mass accretion rate of the order of a hundred days, and a high observed X-ray luminosity. We interpret this new association using an isotropic emission model, where neutrinos are produced by the collision of accelerated protons with infrared photons. After accounting for the high redshift of AT2021lwx (by interpreting the data in the supermassive black hole (SMBH) frame), we find that the expected neutrino fluences and neutrino time delays are qualitatively comparable to the other TDEs. Since data are only available up to 300 days postpeak in the SMBH frame, significant uncertainties exist in the dust echo interpretation, and therefore in the predicted number of neutrinos detected, Nν≃3.0×10−3−0.012 . We recommend further follow-up of this object for an extended period and suggest refining the reconstruction of the neutrino arrival direction in this particular case.

The “Magnificent Seven” X-Ray Isolated Neutron Stars Revisited. I. Improved Timing Solutions and Pulse Profile Analysis

We present the first systematic X-ray pulse timing analysis of the six members of the so-called “Magnificent Seven” nearby thermally emitting isolated neutron stars (XINS) with detected pulsations. Using the extensive collection of archival XMM-Newton, Chandra, and NICER observations spanning over two decades, we obtain the first firm measurement of the spin-down rate for RX J2143.0+0654, while for the rest we improve upon previously published spin ephemerides and extend them by up to an additional decade. Five of the XINS follow steady spin-down with no indication of major anomalies in their long-term timing behavior; the notable exception is RX J0720.4−3125, for which, in addition to confirming the previously identified glitch, we detect a second spin derivative. The high-quality folded X-ray pulse profiles produced with the updated timing solutions exhibit diverse and complex morphologies, as well as striking energy dependence. These peculiarities cannot be readily explained by blackbody-like isotropic emission and simple hot-spot configurations, hinting at the presence of complex multitemperature surface heat distributions and highly anisotropic radiation patterns, such as may arise from a strongly magnetized atmospheric layer.

Escape probability for isotropic emitters near Kerr black hole with astrometric

The paper investigates the escape probability for isotropic emitters near a Kerr black hole. We propose a new approach to obtain the escape probability in a general manner, going beyond previous case-by-case studies. This approach is based on studies of the black hole shadow with astrometric observable and can be applied to emitters with an arbitrary 4-velocities and locations, even to the emitters outside of the equatorial plane. We also consider representative examples illustrating how escape probabilities vary with distance, velocity, and inclination angle. Overall, this new approach provides an effective method for studying escape probabilities near Kerr black holes.

Search for Gravitational-wave Transients Associated with Magnetar Bursts in Advanced LIGO and Advanced Virgo Data from the Third Observing Run

Gravitational waves are expected to be produced from neutron star oscillations associated with magnetar giant flares and short bursts. We present the results of a search for short-duration (milliseconds to seconds) and long-duration (∼100 s) transient gravitational waves from 13 magnetar short bursts observed during Advanced LIGO, Advanced Virgo, and KAGRA’s third observation run. These 13 bursts come from two magnetars, SGR 1935+2154 and Swift J1818.0−1607. We also include three other electromagnetic burst events detected by Fermi-GBM which were identified as likely coming from one or more magnetars, but they have no association with a known magnetar. No magnetar giant flares were detected during the analysis period. We find no evidence of gravitational waves associated with any of these 16 bursts. We place upper limits on the rss of the integrated incident gravitational-wave strain that reach 3.6 × 10−23 /Hz at 100 Hz for the short-duration search and 1.1 × 10−22 /Hz at 450 Hz for the long-duration search. For a ringdown signal at 1590 Hz targeted by the short-duration search the limit is set to 2.3 × 10−22 /Hz . Using the estimated distance to each magnetar, we derive upper limits on the emitted gravitational-wave energy of 1.5 × 1044 erg (1.0 × 1044 erg) for SGR 1935+2154 and 9.4 × 1043 erg (1.3 × 1044 erg) for Swift J1818.0−1607, for the short-duration (long-duration) search. Assuming isotropic emission of electromagnetic radiation of the burst fluences, we constrain the ratio of gravitational-wave energy to electromagnetic energy for bursts from SGR 1935+2154 with the available fluence information. The lowest of these ratios is 4.5 × 103.

Efficiency of Nonthermal Pulsed Emission from Eight MeV Pulsars

We report on the properties of pulsed X-ray emission from eight MeV pulsars using XMM-Newton, NICER, NuSTAR, and HXMT data. For five of the eight MeV pulsars, the X-ray spectra can be fit by a broken power-law model with a break energy of ∼5–10 keV. The photon indices below and above the break energy are ∼1 and ∼1.5, respectively. In comparison with the X-ray emission of the Fermi-LAT pulsars, the MeV pulsars have a harder spectrum and a higher radiation efficiency in the 0.3–10 keV energy bands. When isotropic emission is assumed, the emission efficiency in the keV–MeV bands is estimated to be η MeV ∼ 0.01–0.1, and this is similar to the efficiency of the GeV emission of the Fermi-LAT pulsars with a similar spin-down power. To explain the observed efficiency of the MeV pulsars, we estimate the required pair multiplicity as 104–7, which depends on the emission process (curvature radiation or synchrotron radiation) and on the location in the magnetosphere. The high multiplicity indicates that the secondary pairs that are created by a pair-creation process of the GeV photons produce the X-ray/soft gamma-ray emission of the MeV pulsars. We speculate that the difference between MeV pulsars and Fermi-LAT pulsars can be attributed to the difference in viewing angle measured from the spin axis if the emission originates from a region inside the light cylinder (canonical gap model) or to the difference in the inclination angle of the magnetic axis if the emission is produced in the equatorial current sheet outside the light cylinder.

Shadows and photon rings of a quantum black hole

Recently, a black hole model in loop quantum gravity has been proposed by Lewandowski, Ma, Yang and Zhang (2023) [34]. The metric tensor of the quantum black hole (QBH) is a suitably modified Schwarzschild one. In this paper, we calculate the radius of the circular null geodesic (light ring) and obtain the linear approximation of it with respect to the quantum correction parameter α: rl≃3M−α9M. We then assume the QBH is backlit by a large, distant plane of uniform, isotropic emission and calculate the radius of the black hole shadow and its linear approximation: rs=33M−α6(3M). We also consider the photon ring structures in the shadow when the impact parameter b of the photon approaches to a critical impact parameter bc, and obtain a formula for estimating the deflection angle, which is φdef=−2ωrl2log⁡(1−bc/b)+C˜(bc). We also numerically plot the images of shadows and photon rings of the QBH in three different illumination models and compare them with that of a Schwarzschild black hole. It is found that we could distinguish the quantum black hole with a Schwarzschild black hole via the shadow images in certain illumination models.

Spectral and type I X-ray burst studies of 4U 1702−429 using AstroSat observations

ABSTRACT 4U 1702−429, an atoll-type neutron star low-mass X-ray binary, was observed twice by the AstroSat/Soft X-ray Telescope (SXT) and Large Area X-ray Proportional Counters (LAXPC-20) on 2018 April 27 and 2019 August 8. Persistent emission spectra of the source were well fitted with the model combination - constant × tbabs (thcomp × diskbb+powerlaw). The parameters obtained from the spectral analysis revealed the source to be in a hard spectral state during the observations. Time-resolved spectral analyses were performed on the three type I X-ray bursts detected from the source. Burst analysis showed that the source underwent a photospheric radius expansion. Consequently, the radius of the neutron star and distance to the source (with isotropic and anisotropic burst emission) were obtained as 12.65$\substack{+0.90\\-0.86}$ km and 6.92$\substack{+0.16\\-0.09}$ and 8.43$\substack{+0.20\\-0.10}$ kpc, respectively.

Inverse Compton Emission and Cooling of Relativistic Particles Accelerated at Shear Boundary Layers in Relativistic Jets

Both observational evidence and theoretical considerations from magnetohydrodynamic simulations of jets suggest that the relativistic jets of active galactic nuclei (AGN) are radially stratified, with a fast inner spine surrounded by a slower-moving outer sheath. The resulting relativistic shear layers are a prime candidate for the site of relativistic particle acceleration in the jets of AGNs and gamma-ray bursts (GRBs). In this article, we present outcomes of particle-in-cell simulations of magnetic-field generation and particle acceleration in the relativistic shear boundary layers (SBLs) of jets in AGNs and GRBs. We investigate the effects of inverse Compton cooling on relativistic particles that are accelerated in the SBLs of relativistic jets, including the self-consistent calculation of the radiation spectrum produced by inverse Compton scattering of relativistic electrons in an isotropic external soft photon field. We find that the Compton cooling can be substantial, depending on the characteristic energy (blackbody temperature and energy density) of the external radiation field. The produced Compton emission is highly anisotropic and more strongly beamed along the jet direction than the characteristic 1/Γ pattern expected from intrinsically isotropic emission in the comoving frame of an emission region moving along the jet with a bulk Lorentz factor Γ. We suggest that this may resolve the long-standing problem of the Doppler factor crisis.

Bipolar outflows out to 10 kpc for massive galaxies at redshift z ≈ 1.

Galactic outflows are believed to play a critical role in the evolution of galaxies by regulating their mass build-up and star formation1. Theoretical models assume bipolar shapes for the outflows that extend well into the circumgalactic medium (CGM), up to tens of kiloparsecs (kpc) perpendicular to the galaxies. They have been directly observed in the local Universe in several individual galaxies, for example, around the Milky Way and M82 (refs. 2,3). At higher redshifts, cosmological simulations of galaxy formation predict an increase in the frequency and efficiency of galactic outflows owing to the increasing star-formation activity4. Galactic outflows are usually of low gas density and low surface brightness and therefore difficult to observe in emission towards high redshifts. Here we present an ultra-deep Multi-Unit Spectroscopic Explorer (MUSE) image of the mean Mg II emission surrounding a sample of galaxies at z ≈ 1 that strongly suggests the presence of outflowing gas on physical scales of more than 10 kpc. We find a strong dependence of the detected signal on the inclination of the central galaxy, with edge-on galaxies clearly showing enhanced Mg II emission along the minor axis, whereas face-on galaxies show much weaker and more isotropic emission. We interpret these findings as supporting the idea that outflows typically have a bipolar cone geometry perpendicular to the galactic disk. We demonstrate that this CGM-scale outflow is prevalent among galaxies with stellar mass M* ≳ 109.5M⊙.

Spectral and Timing Study of the Newly Detected Ultraluminous X-Ray Sources in NGC 3585 Using Different Chandra Observations.

The present work aims to study the previously unstudied Ultraluminous X-ray sources (ULXs) in the galaxy NGC 3585 at its various epochs of Chandra observation. We report here the detection of two new ULXs viz. CXOUJ111306.0-264825 (X-1) and CXOUJ111325.3-264732 (X-2) with their bolometric luminosity > 1039erg s−1 in its various Chandra observations. X-1 was found to be a spectrally hard ULX in both the epochs where it was detected. However in the ULX, X-2, a slight hardening of the spectra was observed within a period of 17 years. Assuming isotropic emission and explained by disk blackbody model, the spectrally softer epoch of X-2 with an inner disk temperature, kTin ∼ 0.79 keV and bolometric luminosity ∼ 2.51 × 1039erg s−1 implies for X-2 to be powered by a compact object, necessarily a black hole of mass, MBH ∼ 44.85+82.11−25.92M⊙ accreting at ∼ 0.42 times the Eddington limit. The Lightcurve of X-1 and X-2 binned at 500s, 1ks, 2ks and 4ks has shown no signature of short-term variability in both the ULXs in kilo-seconds time scales. Overall, both the detected ULXs seem to be almost static sources both in long-term (years) as well as short-term (kilo-seconds) time scales with the presently available Chandra Observations.

X-ray polarization properties of partially ionized equatorial obscurers around accreting compact objects

ABSTRACT We present the expected X-ray polarization signal resulting from distant reprocessing material around black holes. Using a central isotropic power-law emission at the centre of the simulated model, we add distant equatorial and axially symmetric media that are covering the central accreting sources. We include partial ionization and partial transparency effects, and the impact of various polarization and steepness of the primary radiation spectrum. The results are obtained with the Monte Carlo code STOKES that considers both line and continuum processes and computes the effects of scattering and absorption inside static homogenous wedge-shaped and elliptical toroidal structures, varying in relative size, composition and distance to the source. We provide first order estimates for parsec-scale reprocessing in Compton-thin and Compton-thick active galactic nuclei, as well as winds around accreting stellar-mass compact objects, for observer’s inclinations above and below the grazing angle. The resulting reprocessed polarization can reach tens of per cent with either parallel or perpendicular orientation with respect to the axis of symmetry, depending on subtle details of the geometry, density, and ionization structure. We also show how principal parameters constrained from X-ray spectroscopy or polarimetry in other wavelengths can lift the shown degeneracies in X-ray polarization. We provide an application example of the broad modelling discussion by revisiting the recent IXPE 2–8 keV X-ray polarimetric observation of the accreting stellar-mass black hole in Cygnus X-3 from the perspective of partial transparency and ionization of the obscuring outflows.

Shape-tailored whispering gallery microcavity lasers designed by transformation optics

Semiconductor microdisk lasers have great potential as low-threshold, high-speed, and small-form-factor light sources required for photonic integrated circuits because of their high-Q factors associated with long-lived whispering gallery modes (WGMs). Despite these advantages, the rotational symmetry of the disk shape restricts practical applications of the photonic devices because of their isotropic emission, which lacks directionality in far-field emission and difficulty in free-space out coupling. To overcome this problem, deformation of the disk cavity has been mainly attempted. However, the approach cannot avoid significant Q degradation owing to the broken rotational symmetry. Here, we first report a deformed shape microcavity laser based on transformation optics, which exploits WGMs free from Q degradation. The deformed cavity laser was realized by a spatially varying distribution of deep-sub-wavelength-scale (60 nm diameter) nanoholes in an InGaAsP-based multi-quantum-well heterostructure. The lasing threshold of our laser is one-third of that of the same shaped homogeneous laser and quite similar to that of a homogeneous microdisk laser. The results mean that Q spoiling caused by the boundary shape deformation is recovered by spatially varying nanohole density distribution designed by transformation optics and effective medium approximation.

Upper bounds on technoemission rates from 60 years of “silence”

The lack of detection to date of electromagnetic technosignatures implies either that we have been unable to detect them due to incomplete sampling of the search space or that we cannot detect them because the Earth has been located during the entire history of SETI in a region of space not covered by artificial extraterrestrial emissions. Starting from the latter hypothesis, and assuming that technoemissions are generated in our galaxy at a constant rate Γ, we derive probabilistic upper bounds on Γ. In the case of isotropic emissions, we find a 95 % probability that there are less than one to five emissions per century that are generated across the entire Milky Way. This implies that there is a 50 % probability that the Earth will not be illuminated by technosignals for at least the next 60 to 1800 years. We show that higher emission rates can only be derived under the assumption that a significant fraction of all technoemissions are anisotropic and randomly oriented narrow beams, without however systematically changing the waiting time until the next technosignal reaches Earth.

Single-Fiber Transducer Arrays for 3-D Ultrasound Computed Tomography: From Requirements to Results

A potential method for future breast cancer screening is 3D ultrasound computed tomography (USCT). The utilized image reconstruction algorithms require transducer characteristics fundamentally different from conventional transducer arrays, leading to the necessity of a custom design. This design has to provide random transducer positioning, isotropic sound emission as well as a large bandwidth and wide opening angle. In this paper, we present a new transducer array design to be utilized in a third generation 3D USCT system. Each system requires 128 cylindrical arrays, mounted into the shell of a hemispherical measurement vessel. Each new array contains a 0.6 mm thick disk with 18 single PZT fibers (0.46 mm diameter) embedded in a polymer matrix. Randomized positioning of the fibers is achieved with an arrange-and-fill process. The single-fiber disks are connected on both ends with a matching and backing disk using simple stacking and adhesives. This enables fast and scalable production. We characterized the acoustic field of 54 transducers with a hydrophone. Measurements in 2D showed isotropic acoustic fields. The mean bandwidth and opening angle are 131% and 42°, respectively (both -10 dB). The large bandwidth arises from two resonances within the utilized frequency range. Parameter studies using different models showed that the realized design is already close to the achievable optimum for the transducer technology used. Two 3D USCT systems were equipped with the new arrays. First images show promising results, with an increase in image contrast and a significant reduction of artifacts.

Lightning radiometry in visible and infrared bands

Calibrated measurements of lightning optical emissions are critical for both quantifying the impacts of lightning in our atmosphere and devising detection instruments with sufficient dynamic range capable of yielding close to 100% detection efficiency. However, to date, there is only a limited number of investigations that have attempted to take such calibrated measurements. In this work, we report the power radiated by lightning in both visible and infrared bands, assuming isotropic emission, and accounting for atmospheric absorption. More precisely, we report peak radiated power and total radiated energy in the combined visible plus near-infrared range (VNIR, 0.34–1.1 μm), around the Hα line (652–667 nm), and for the 2–2.5 μm infrared band. The estimated peak power and total energy radiated by negative cloud-to-ground return strokes in the VNIR range is 130 MW and 20 kJ, respectively. Additionally, we detected peak radiated powers of 12 and 0.19 MW in the Hα and infrared bands, respectively. We cross-reference the optical data set with peak current reported by a lightning detection network. The resulting trend is that optical power emitted around the Hα line scales with peak return stroke current according to a power law with exponent equal to 1.25. This trend, which should be approximately true across the entire visible spectrum, can be attributed to the plasma negative differential resistance of the lightning return stroke channel. We conclude by discussing the challenges in performing calibrated measurements of lightning optical power in different bands and comparing the results with previously-collected data with different experimental setups, observation conditions, and calibration methods.

Inverse Altermagnetic Spin Splitting Effect‐Induced Terahertz Emission in RuO2

AbstractThe relativistic inverse spin Hall effect (ISHE) plays a pivotal role in terahertz (THz) emission in magnet/heavy metal bilayers. Here, THz emission from RuO2/Py bilayers is reported due to not only the relativistic ISHE but also the nonrelativistic inverse altermagnetic spin splitting effect (IASSE) in RuO2. For the (100)‐oriented RuO2/Py bilayers, the THz emission is greatly enhanced owing to IASSE once the polarization direction of the spin current (from the Py layer induced by pump laser) is parallel to the Néel vector of RuO2, producing the anisotropic THz emission with twofold symmetry. In contrast, the RuO2(110)/Py bilayer only exhibits isotropic THz emission because of the absence of IASSE‐induced spin‐charge conversion in the (110)‐oriented RuO2 films. Apart from the fundamental significance of exploring the IASSE‐induced spin‐to‐charge conversion, the finding also enriches the physical mechanism and modulation method of THz emission in spintronic systems.

Development of a stand-alone precalculated Monte Carlo code to calculate the dose by alpha and beta emitters from the Ra-224 decay chain.

Recent developments in alpha and beta emitting radionuclide therapy highlight the importance of developing efficient methods for patient-specific dosimetry. Traditional tabulated methods such as Medical Internal Radiation Dose (MIRD) estimate the dose at the organ level while more recent numerical methods based on Monte Carlo (MC) simulations are able to calculate dose at the voxel level. A precalculated MC (PMC) approach was developed in this work as an alternative to time-consuming fully simulated MC. Once the spatial distribution of alpha and beta emitters is determined using imaging and/or numerical methods, the PMC code can be used to achieve an accurate voxelized 3D distribution of the deposited energy without relying on full MC calculations. To implement the PMC method to calculate energy deposited by alpha and beta particles emitted from the Ra-224 decay chain. The GEANT4 (version 10.7) MC toolkit was used to generate databases of precalculated tracks to be integrated in the PMC code as well as to benchmark its output. In this regard, energy spectra of alpha and beta particles emitted by the Ra-224 decay chain were generated using GAMOS (version 6.2.0) and imported into GEANT4 macro files. Either alpha or beta emitting sources were defined at the center of a homogeneous phantom filled with various materials such as soft tissue, bone, and lung where particles were emitted either mono-directionally (for database generation) or isotropically (for benchmarking). Two heterogeneous phantoms were used to demonstrate PMC code compatibility with boundary crossing events. Each precalculated database was generated step-by-step by storing particle track information from GEANT4 simulations followed by its integration in a PMC code developed in MATLAB. For a user-defined number of histories, one of the tracks in a given database was selected randomly and rotated randomly to reflect an isotropic emission. Afterward, deposited energy was divided between voxels based on step length in each voxel using a ray-tracing approach. The radial distribution of deposited energy was benchmarked against fully simulated MC calculations using GEANT4. The effect of the GEANT4 parameter StepMax on the accuracy and speed of the code was also investigated. In the case of alpha decay, primary alpha particles show the highest contribution (>99%) in deposited energy compared to their secondary particles. In most cases, protons act as the main secondary particles in the deposition of energy. However, for a lung phantom, using a range cutoff parameter of 10µm on primary alpha particles yields a higher contribution of secondary electrons than protons. Differences between deposited energy calculated by PMC and fully simulated MC are within 2% for all alpha and beta emitters in homogeneous and heterogeneous phantoms. Additionally, statistical uncertainties are less than 1% for voxels with doses higher than 5% of the maximum dose. Moreover, optimization of the parameter StepMax is necessary to achieve the best tradeoff between code accuracy and speed. The PMC code shows good performance for dose calculations deposited by alpha and beta emitters. As a stand-alone algorithm, it is suitable to be integrated into clinical treatment planning systems.